(Thp  9.  li.  HtU  ICtbrary 


f>EClAL  C0LLECT1 


G57 


North  (Earoltna  l^tatp  HmnprBitii 


Z.  SMITH  REYNOLDS 
FOUNDATION 

COLLECTION   IN 
SCIENCE  AND  TECHNOLOC3Y 


r-f 


TREATISE 

ON 

g0nter's  scale,  and  the  sliding 

RULE  : 

TOGETHER  WITH  A 

DESCRIPTION  AND  USE, 

OF  THfi 

SECTOR,  PROTRACTOR,  PLAIN  SCALE,  AND 
LINE  OF  CHORDS  ; 

OR, 

AN  EASY  METHOD  OF  FINDING  THE  AREA  OP,§tPER- 

FlCES  ;     AND  OF  MEASURING  BOARDS  ;     AND  OF 

FINDING  THE  SOLID  CONTENTS  OF  BODIES, 

ESPECIALLY  THAT  OP  TIMBER,  BY  THE 

SLIDING  rule;     and  ALSO  OF  GUA- 

GING  CASKS,  AND  ROUND  TIMBER. 

TO  THESE  ARE   ADDED   SEVERAL   USEFUL    LOGAAITHMIt 

BLES,    TABLES    OF     LATITUDE    AND    DEPARTURE,    AND    A 

TABLE  OF    NATURAL    RADII,  NOT    KNOWN    TO    HAVj: 

BEEN  HERETOFORE  PUBLISHED  :    ALSO  A  TABLE 

OF  ROUND,  AND  SQUARE  TIMBER. 


"BY  GEORGE  CURTIS,  MATH. 


WHITEHALL,  N.  Y. 
r"R!NTEO  AND  PUBLISHED  BY  E.  ADAM!^* 

1824. 


r)Lsirid  of  yutTcni^ — Tv  Wit. 

BE  IT  REMEMBERED,  That  on  V^e  tw  entv-cevent'a  (Tnjir 
of  May  in  the  forty-ei^jhth  year  of  the  independence  of  th^ 
Cnited  States  of  America,  George  Ctrtis  of  the  said  district-, 
jiath  deposited  in  this  office  the  title  of  a  book,  the  rii:ht  whereof  he 
I  laiais  as  authiT,  in  the  words  following,  to  wit :  "A  treatise  on 
(inntei'*'3  Scale,  and  the  ?lidin§^  Rule,  together,  with  a  description 
n  ad  use  of  the  Sector,  the  Protractor,  Plain  Scale,  and  Line  cf 
i.'horJa  ;  or  an  ea*ry  method  ef  llndin^  the  area  of  superfices.  and  of 
measuring  Boards  and  finding;  the  solid  eentents  of  bodies,  especially 
ihat  of  tiniber,  by  the  Sliding  Rule,  and  al«o  of  g;auginj  Casks  and 
Round  Timber.  To  these  are  added  several  useful  Log;arithmick  Ta- 
bles, Tables  of  Latitude  and  Departure,  and  a  table  of  .Natural  Radii, 
uot  known  to  be  heretofore  published.  By  George  Curtis, 
Tvlath."  In  conformity  to  the  Act  of  Congress  of  the  United  States, 
e;:titled  "  an  act  fur  the  encouragment  of  learning,  by  securing  tlie 
«  opies  of  maps,  cnarts  and  books  to  the  authors  and  proprietors  «?f 
5  loh  copies,  duriHg  tlie  times  therein  mentioned."" 

JESSE  GOVE, 
Clerk  of  th.t  District  of  Fermont. 
A  i»*!t  C'Vhy  r^f  ReCi?rd,  exafnln^jd  and  sidled  by 

J.  GOVE,  CZf 7*, 


^(P{:2^4U.^*4^ 


PREFACE, 

The  primary  design  of  this  Treatise,  is  to  introduic  a 
more  general  attention  to,  and  knowledge  of  the  instruments 
herein  described.  Notwithstanding  the  many  books  that 
are  daily  issuing  from  the  press,  on  other  subjects,  yet 
I  have  known  of  none  that  can  preclude  the  benefits  of  a 
work  of  this  kind.  The  author  was  led  into  these  views 
by  journeying  through  many  parts  of  the  United  States,  and 
finding  n  work  on  the  subject  here  treated  of,  very  much 
needed.  It  is  designed  as  a  pocket  companion,  for  the 
Surveyor,  Blechanick,  and  for  those  who  deal  in  timber 
and  boards,  particularly  by  its  tables  of  round  and  square 
timber,  for  the  Wheelright,  the  Housecarpenter,  Joiner, 
Cooper,  and  many  other  Dealers  and  Craftsmen,  as  well  as 
the  Grocer,  for  gauging  expeditiously.  How  fitr  the  au- 
thor has  succeeded  in  his  views,  and  endeavours  to  ren- 
der it  useful  tb  mankind,  must  be  decided  by  the  test  ii 
experience. 


RECO.AhviENDATIONS. 


Haviog  duly  examined  the  inclossd  W0rk,in  maniiscript.. 
am  constrained  and  deem  it  proper,  to  recommend  it  to  the 
patronage  of  a  genereus  publick,  as  being  a  valuable  and 
useful  production  :  valuable  from  its  tendency,  to  bring  in- 
to general  Bse,  that  which  has,  hitherto,  been  known  to  but 
few  ;  useful,  in  vastly  abridging  the  labour  of  Arithmetical 
and  Mathematical  calculations,  that  the  surveyor  and  artist 
"have  frequently  to  make,  also  in  containing  some  things, 
never  before  known  to  have  been  published. 

CYRUS  CARPENTER, 
Physician f  and  Math e mat iciau-^ 
'Whiting,  Vt.  May  24,  1824. 


Having  been  thoroughly  convinced  by  ddiVy  experience 
aat  a  work  like  the  present  was  much  needed  as  well  by 
ihe  mechanick  va  by  the  mathematician  and  the  surveyor, 
!t  was  with  no  inconsiderable  degree  of  interest  that  I  gave 
it  a  perusal.  After  having  attentively  and  minutely  exan^- 
jued  it,  I  find  that  the  author  has  correctly  anticipated  the 
detects  of  works  of  this  description  in  use,  and  has  admira- 
bly supplied  them.  He  has  not  only  very  much  abridged 
ine  labour  of  many  mathematical  estimations  ;  and  simplified 
}nauy  processes  which  were  formerly  tedious  and  perplex- 
ing ;  but  has  embodied  in  his  work  many  interesting  facts 
which  are  original ;  or  at  least  not  to  be  found  in  similar 
productions.  Upon  the  whole,  I  consider  the  work  well 
calculated  to  promote  the  interests  of  mathematical  sci- 
»!nce,  and  sincerely  hope  it  will  meet  with  that  liberal 
reception  from  an  intelligent  publickj  which  its  merits  de- 
ierye. 

SAMUEL  BEACH,  County  Surveyor. 

Addison  County,  Vt, 


We.  the  subscribers,  have  perused  with  some  degree 
jf  pleasure,  a  Treatise  on  Gunter's  Scale,  Lc.  prepared 
■tr  the  press,  by  George  Curtis,  and  have  minutely  exam- 


HECOMMEJ^DATIOjXS,  5 

sued  that  part  which  relates  to  the  measurment  of  timber 
and  boards  by  the  Shding  Rule,  and  do  cheerfully  recom- 
mend it  as  being  an  easy  and  concise  way  of  getting  the 
contents  of  solid  bodies  of  every  description  ;  and  the 
ready  calculated  tables  of  round  and  square  timber  which 
never  have  appeared  in  any  work  of  this  kind,  cannot  fail 
to  render  it  valuable  to  all  those  who  deal  in  lumber. 

ISAAC  COLLINGS, 

Inspector  of  Lumber. 

ASA  EDDY. 
Whitehall  August  24,  1824. 


A2 


39 

0 

39 

T 

J 

/          / 

^/\ 

/ 

FIO  !st. 

60 

1 

o 

50 

40 
30 

^ 

% 

1      D 

^''^^ 

^ 

^^^-"""n*^ 

/90 

\7^ 

r^ 

^^ 

/       /^^ 

y<b    80 

70 

1  50 

§  40 
H 

fi30 
« 
w  20 

V 

/ 

K 

< 

< 

\ 

1 

\/^ 

10 

Sin 

68 

> 

A  Versed  Sines  C        10 

110  170  160  150  140  130  120  110  100  &0      gO 


20     SO     40     50  60«o?B 
70     60     50    ^  30 


'             '             '              . 

cc 

^ 

GO 

o 

po 

H 

> 

i-rt 

t— 1 

_^ 

j 

~  o 

1 

-B 

— 

©     - 

-  o     - 

-  o 

— 

I-* 

-  ^ 

o 

- 

^  ' 

-S   - 

C3 

-8 

- 

hd 

w      - 

"  o 

-B 

— 

C9 

~  o 

o 

o 

_  lt». 

-J 

~ 

o 

>;^ 

-  o 

»5 

CO 

—  o 

- 

^  - 

:s  - 

o 

_ 

tfi 

-s 

_ 

o 

- 

<3> 

N^ 

CTT           - 

-g 

*3 

—  o 

o 

-  » 

o 

.u 

o 

-  o 

CO 

o 

_C5 

H-t 

"■"    ^^ 

o 

- 

-  v» 

~  ^s 

_ 

§ 

o 

" 

- 

-  o> 

o 

i 

^ 

' 

1 

1 

»T5 

> 


C/2 

o 


> 
o 
o 

CO 

> 
w 

o 


CONSTRtCTION  OP  THE  PLAIN 
SCALE. 

1.  With  the  rac^ius  intended  for  the  scale,  describe  a  se- 
micircle, (see  plate  1st  fig  lit.)  and  from  the  ctntre  C, 
draw  CD,  perpendicular  to  AB,  which  will  divide  the  se- 
micircle into  two  quadrants,  AD,  BD  ;  continue  CD  to- 
wards S,  draw  BT,  perpendicular  to  CB,  and  join  BD  and 
AD. 

2.  Divide  the  quadrant  BD  into  9  equal  parts,  then  each 
of  these  divisions  will  be  10  degrees.  S^ubdi>ide  each  of 
these  parts  into  single  degrees,  and  if  your  radius  will  ad- 
mit of  it,  into  minutes,  or  some  equal  parts  of  a  degree, 
larger  than  a  minute. 

3.  Set  one  foot  of  the  compasses  at  B,  and  transfer  each 
of  the  divisions  of  the  quadrant  BD,  to  the  right  line  BD, 
then  BD  will  be  a  Line  of  Chords. 

4.  Then  the  points,  10,  20,  30,  kc.  in  the  quadrant  BD, 
draw  right  lines,  parallel  to  CD,  to  cut  the  radius  CB,  and 
they  will  divide  that  line  into  a  line  of  sines,  which  muni 
be  numbered  from  C  towards  B. 

5.  If  the  same  line  of  sines  be  numbered  from  B  towards 
C  it  will  become  a  Ime  of  versed  sines,  which  may  be  con- 
tinued to  loO  degrees,  if  the  same  divisions  be  transferred 
on  the  same  line  on  the  other  side  of  the  centre  C. 

6.  From  the  centre  C,  through  the  several  divisions  of 
the  quadrant  BD,  draw  right  lines  till  they  cut  the  tangent 
BT  so  the  line  BT,  will  become  a  Line  of  Tangents.* 

7.  Set  one  foot  of  the  compasses  at  C,  extend  the  other 
to  the  several  divisions,  10,  20,  SO,  k.c.  in  the  tannent 
line  BT,  and  transfer  these  extents,  severally,  to  the  right 
line  CS,  then  that  line  will  be  a  Line  of  Secants. 

8.  Right  lines  draw  from  A  to  the  several  divisions   10, 

*  A  mistake  -was  made  in  engraving  this  plate.  The  lints  run- 
liin*  parallel  -^'ith  C  D,  and  the  curved  lines  between  B  D,  and  the 
lines  falling  from  the  Tangents  should  intersect  each  other  on  tlic 
semicircle  A  D  B  ;  and  tlelast  meatioued  Jiaes  jbould  run  in  a  di 
rection  to  centre  at  C. 


^  THE  PLALX  SCALi:.  \  i 


\^;ft 


;l't^.^),  4o,  iic.  in  the  quadrant  BD  niH  divide  the  the  ra- 
dios CD  into  a  hne  of  semi-tansents. 

^.   Divide  the  q^iadrant  AD  into  0  cqnal  parts,  and  from 
A  as   a  centre,  transfer  these    divisions   severally   into   the 
3ine  AD, 'then  AD  will  be  a  Line  of  Rhonibs,  each  division 
answering  1 1  degrees  and  13  minutes  upon  the   Line   of 
Chords.     The  use  of  this  division,  or  line,  is  for  measuring 
angles,  and  protracting  them,  according  to  the  common  di- 
visions of  the  Mariner's   Compass.     If  the   radius  AC  be 
divided    into    100,    or    1000,  &c.   equal -parts,  and   the 
length  of  the  several  sines,  tangents,  and  secants,  corrod- 
ponding  to  the  several  arches  ot  the  quadrant,  be  measured 
ti*ereby,  and  these  numbers  set  down   in   a  table,  each  in 
its  proper  column,  you  will  by  these  measures  have  a  col- 
lection of  numbers,  by  which  the  several  cases  in   Trigo- 
nometry, may  be  solved.     Rigbt  lines,  graduated  as  above 
mentioned,  being  placed  severally  upon  the  Rule,  form  the 
instrument  called  the  Plain  Scale,  (see  plate  1st  fig  2d,)  by 
which  the  line  and  argles  of  all  triangles  may  be  measured. 
All  right  lines  a?  the  sides  of  plain  triangles,  &c.  wh-Bn  they 
are  considered  simply  as  such,  without  having  relation  to 
a  circle,  are  measured   by   scales   of  equal  parts,  each  of 
which  is  subdivided   into   ten  equal  parts  :  and  this  serves 
as  the  common  divisions  to  all  the  rest.     In  most  Scales,  an 
inch  is  taken  for  a  common  measure,  and  whatever  an  inch 
is  divided  into,  may  be  found  at  the  end  of  the  Scale  :  di- 
vided in  this  manner,  any  number  less  than    100,  may  be 
readily  taken.     But  if  the  number  should  consist  of  three 
places  of  t3gures,  the  value  of  the  third   figure,  cannot  be 
exactly  ascertained  ;  and   in  this  case,  it  i«  better  to  use  a 
Diagonal  Scale,  by  which  any  number  consisting  of  three 
places  of  figures,  m?ty  be  exactly  found.     The^'figure?  of 
this  Scale  are  given  in  plate  1st,  fig  3d  ;  its   construction  is 
as   follows :    Having   prepared   a   ruler   of  a   convenient 
breadth  for  your  Scale,  draw  near  the  edges,  two  right 
lines,  AF,  CC,  parallel  to  each  other  ;   divide  one  of  these 
imes,  as  Fx\  into  equal  parts,  according  to  the  size  of  your 
^>cale,  and  through  eacii  of  these  divisions,  draw  riirht  lin^s 
perpendicular  to  Ai\  to  meet  CC,  then  divide  the  breadia 
into  ten  equal  parts  ;  and  through  each  of  these  divisions 
e'ravT  ri^^ht  lines,  parallel  to  AF  and  CC.     Divide  the  hoes 
AB,  CDj  irito  teti  e<iu»}  parts,  and  from  the  poiat  A  lo  tb'' 


12  mE  SLIDLVG  RULE. 

first  division  in  the  line  CD,  draw  a  right  line,  parallel  t& 
that  line  ;  draw  right  line*  through  all  their  divisions,  and 
the  Scale  is  finished. 

Befities  the  line?  already  mentioned,  ther€  is  another  on 
some  Scales,  and  on  the  Gunter's  Scale,  marked  ML, 
which  is  joined  to  a  line  of  chords,  and  shows  how  many 
miles  of  Easting  and  Westing  corresponds  to  a  degree  of 
Longitude  in  every  degree  of  Latitude.*  These  several 
hnes  are  generally  put  on  one  side  of  a  P«.ule  two  feet  long, 
and  on  the  other  side  is  laid  down  a  scale  ©f  Logarithms  of 
the  sine  taogents  and  nun»hers,  which  is  commonly  called 
Guater's  Scile,  and  as  it  is  of  general  use,  it  requires  a 
particular  de-cription,  which  will  be  found  on  the  thir- 
teenth page. 

*  As  it  wo  :1 !  ccafusc  the  adjoined  fignrei  to  describe  on  it  the 
line  of  Lou^^tuile,  it  is  neglected ;  but  the  ocnstrjction  is  a«  follows  : 
diriie  the  line  C  B,  inio  60  e>raal  parts,  and  throui-h  each  point  draw 
lines  parallel  to  CD  to  inter^^ct  the  arch  BD  Take  B  a»  a  centra 
transfer  the  several  points  of  intersection,  to  the  line  BD,  and  their 
n'ltnber  ii  from  D  towards  B, from  0  to  60,  and  it  will  be  the  Line 
of  Lon'^tude. 


HOW  TO  PROVE  THE  SLIDING  RULE. 

Rule. — Draw  out  the  slider  to  the  right  hand,  till  1  oa 
(he  slider  coincides  with  i  on  the  iised  part,  then  2  on  the 
slider  will  coiuriJe  with  4  on  ike  dxed  part.  Continue  t« 
draw  the  slider  till  1  en  the  slider  coincides  with  3  on  the 
nxed  part,  then  'i  on  the  slider  will  coincide  with  6  on  the 
ttxed  part  :  till  1  on  the  slider  coincides  with  4  on  the  nxe4 
part,  then  2  on  the  slider  will  coincide  with  8  on  the  fixed 
part ;  till  1  coincides  with  5.  then  2  will  coincide  with  the 
centre  I  ;  till  1  coincides  with  5^,  then  2  will  coincide 
with  11  ;  till  1  coincides  with  6.  then  ?  will  coincide  witb 
12  ;  and  thus  rontinue  to  do  till  ycKi  have  gone  through 
the  line,  and  if  the  Rule  is  correctly  graduated,  each  num- 
ber will  correspond  as  above  stated  ;  if  they  do  not  correi- 
pond,  the  Rule  is  oot  cdirect,- atid  c^ynic^nently  will  not 
gire  a  correct  aftswer. 


13 


GUNTER^S  SCALE. 

Gunter*^  Scale  has  upon  it  eight  lines  : 

1.  Sine  Rhombs,  (marked  SR)  corresponding  to  the 
Logarithms  of  Natural  Sines  of  every  point  of  the  Mariner's 
Compass,  numbered  from  the  left  hand  towards  the  right, 
with  1,  2,  3,  4,  5,  6,  7  to  8,  where  is  a  brass  pin  ;  this  line 
is  also  divided,  where  it  can  be  done,  into  halves  and  quar- 
ters. 

2.  Tangent  Rhombs,  (marked  TR)  corrfesponds  to 
the  Loojarithms  of  the  tangents  of  every  point  of  the  Com- 
pass, and  is  numbered  1,  2,  3  to  4,  at  the  right  hand,  where 
there  is  a  pin  ;  and  thence  towards  the  left  hand  with  5,  6, 
7  ;  it  is  also  divided,  where  it  can  be  done,  into  halves  and 
quarters. 

3.  The  line  of  ntimhers,  (marked  NUM)  corresponds 
to  the  Logyriihms  of  numbers,  and  is  marked  thus  :  at  the 
left  hand  it  begi::s  at  1.  and  to\rards  the  right  hand  are  2, 
3,  4,  5,  6,  7,8,  9,.  and  1  in  the  middle  ;  at  which,  is  a 
brass  pin  ;  then  2,  3,  4,  6,  6,  7,  8,  9  and  10  at  the  end, 
where  there  is  another  pin.  Tlie  value  of  these  numbers 
anri  their  intermediate  division,  depends  on  the  estimated 
values  of  the  extreme  numbers,  1  and  10  ;  and  as  this  lint 
is  of  great  importance,  a  particular  description  of  it  and  its 
uses,  will  be  aiven. 

The  first  1,  may  be  counted  for  1,  or  10,  or  100,  or  1000, 
and  then  the  next  2  is  accordingl},  2,  or  20,  or  200,  or 
2000,  &c.  Again,  the  first  1  may  be  reckoned  one  tenth  or 
one  hundredth,  or  one  thousandth  part,  &c.  and  then  the 
next  2  is  two  tenth,  or  two  hundredth,  or  two  thousancltli 
parts,  &c.  &c.  Then,  if  the  first  1,  be  reckoned  1,  the  mid- 
dle 1  is  reckoned  10  and  2,  at  its  right  hand  is  20,  3  is  30, 
4  is  40,  and  10,  at  the  end  is  100  ;  Again,  if  the  first  1  is 
10,  the  next  2  is  20,  3  is  30,  and  so  on,  making  the  middle 
1,^100,  the  next  2  is  200,  the  next  3  is  300,  4  is  400,  and 
10  at  the  end  is  1000.  In  like  manner,  if  the  first  1  be  es- 
teemed one  tenth  part,  the  next  2  is  two  tenth  parts,  and 
the  middle  1  is  one,  and  the  next  2  is  two,  and  10  at  the 
end  is  ten.  Again,  if  the  first  1  be  counted  one  hundredth 
part,  the  next  2  is  two  hundredth  parts,  the  middle  1  is  now 
ten  hundredth  parts,  the  next  two   hundredth  parts,  the 

B 


14  GIWTER'S  SaiLE. 

middle  1  DOW  15  ton    hundredth  parts,   or   one   tenth  parfj 
and  the  nest  2  is  two  tenth  parts,   and    10  at  the  end  is 

counted  1.     As  the  figures  are  iucrea«ed  or  diminished  in 
their  value,  so  in  the  like  manner,   mast  all  the  intermedi- 
ate strokes  or   subdiyisions,  be   increased    or  diramished  ; 
that  is,  if  the  drst  1  at  the   left  hand  be   counted  1,  then  ij 
next  ibllowing   is  2,  arid    each   subtlivision    between   them 
nov?  is  one  tenth  part,  and  so  all  che   wav  to  the  middle  1, 
which  now  is  10,  the  nest  is  20  ; — now   the  longer  strokes 
between  1  and  -   are    to    be    counted    from    the    centre  1, 
(11,  12,)  Inhere  is  a  brass  pin,  then  13.  14,  15,    sometimes 
a  longer  stroke  than  the  rest;   then   16,  17,  18,  19,  20,  at 
the  t]gure  2  ;  and  in  the  Siinie  manner  the  short  strokes  be- 
tween the  ligures  2  and  3,  and   4  and  6,  &c.  are  to  be 
reckoued  as   units.     Again  if  1   at  the  left  hand  be  10,  the 
li^ures  between  It  and  the  Oiiddle  1,  are  common  tens  ;   ana 
the  subdivisions   between   each  tigure  are  units  ;   from  the 
middle    1,  to  10  at  the    end,  each   ri^ure  is   so  many  hun- 
dredths :    and  between  these  ligures  each  longer  diviiion  is 
ten.     From   this  description  it   will  be  easy  to  find  the  di- 
visions   representing   any   given    number  ;    thu«,    suppose 
tije    point   re  ^'resenting  the   number    12,    were    required, 
take  the  division  at  the  figure  1,  in  the  middle  tor  the  dist 
figure  of  12,  then   for  the  second  figure  count  tw©  tenths, 
on  longer    strokes  to    the    right  hand,  and    this   kist  is  the 
point  representing  12,   where   the    brass    pin  is.      Again, 
?uppose  the  number  22,    were   required  ;     the  first  figure 
be^ns  2,  1.     Take  the  division  to  the  figure  2,  and  for  the 
second  figure  2,    couat  two  tenths   onward   and  that  is  the 
point  representing  22,     Again,  suppose  IT-o  were  requir- 
ed.     For  the  firot    fisiure,  1,  take   the   middle  1  :    for  the 
second  figure,  7,  count  onward   as  betare,  and  that  is  170<1', 
and  as  the  remaining  fii^ures  are  28,  or  nearly  oO,  note    the 
point  which  is  nearly  -j^,  lor  the  distance  between  the  marks 
7   and   8,  and  this  will  be  the  point  r€pre5«ntiDg  1720.      If 
^he  point  represeuthng  -iSb  was  required  ;    from  the  4  in  the 
second  intervid  count  towards  5  on  the  right,    three   of  the 
i.crgerdivisir^ns  and  one  of  the  smaller,  (this  smaller  divi>iun 
being  midway  between  the  marks  3  and    4.)  and    that   will 
be  the  division  expressing  435,  and  the  like  of  other  nuia- 
'^ers,  which  by  « little  practice  is  easily  done. 

All  fractions  fouiiJ  m   this  line  m^izt   be  decimal?,  and  ii 


GUA'TER'S  SCALE.  15 

they  are  not,  they  mu«t  be  reduced  to  tlecimals  ;  which 
is  easily  done  by  extending  the  compasses  from  the  denom- 
inator to  the  numerator  ;  that  extent  hiid  the  same  way 
irom  1  in  the  middle  or  right  hand,  will  reach  to  the  deci- 
mal required. 

Example, 

To  find  the  decimal  fraction  eqn:J  to  |-  ;  extend  from 
■1  to  3,  that  extent  will  reach  from  1  on  the  middle  to  75 
towards  the  left  hand  ;  the  hke  may  be  observed  of  any  oth- 
er vulgar  fraction. 

Multiplication  is  performed  on  this  line  by  extending 
from  1  to  the  multiplier,  that  extent  will  reach  from  the 
multiplicand  to  the  product.  Suppose,  for  example,  it 
were  required  to  tind  the  product  of  16  multiplied  by  4  : 
extend  from  1  to  4  ;  that  extent  will  reach  from  16  to  64, 
the  product  required. 

Divsion,  being  the  reverse  of  Multiplication,  therefore, 
extend  from  the  divisor  to  unity  ;  that  extent  will  reach 
from  the  dividend  to  the  quotient.  Suppose  64  to  be  divi- 
ded by  4  ;  extend  from  4  to  1  ;  that  extent  will  reach  from 
64  to  16=  the  quotient. 

Questions  in  the  Rule  of  Three  are  solved  by  this  line, 
as  follows.  Extend  from  the  first  term  to  the  second — that 
extent  will  reach  from  the  third  term  to  the  fourth,  or  an- 
swer. 

It  ought  to  be  particularly  noticed,  that  if  yon  extend 
to  the  left  from  the  first  number  or  term  to  the  second,  yon 
must  also  extend  to  the  left  from  the  third  to  the  fourth, 
and  vice  versa. 

EXAMPLE. 

If  the  diameter  of  a  circle  be  7  inches,  and  the  circum- 
ference 22  inches,  what  is  the  circumference  of  anothdr 
circle,  whose  diameter  is  14  inches  ? 

Extend  from  7  to  22  ;  that  extent  will  reach  from  14  to 
44,  the  same  way. 

The  superficial  contents  of  any  Parallelogram  are  found 
by  extending  from  1  to  the  breadth  ;  that  extent  will  reach 
from  the  length  to  the  superficial  contents. 

EXAMPLE. 

^     Suppose  a  plank  or  board  to  be  15   inches  wide   and  27 
feet  long.     The  contents  are  required. 

Extend  from  1  foot,  to  1  foot  ?  inches,   (or   1,25;)   that 


Id  GUTTER'S  SCALE. 

extent  will  reach   from  27   feet  to  33,75  =  the   fuperncial 
content?.     Or,  you  may  extend  from  12  inches  15,  ^c. 

The  solid  contents  of  any  Bale,  Box,  Chest.  &:c.  is  found 
•>y  extending  from  1  to  the  breadth,  that  extent  will  reach 
.rom  tlie  depth  to  a  fourth  number  ;  and  the  extent  from 
1  to  that  iourth  number,  will  reach  from  the  length  to  the 
solid  contents. 

EXAMPLES. 

1.  What  is  the  solid  contents  of  a  square  pillar,  whose 
length  is  21  feet  9  inches,  breadth  1  foot  3  inches  ? 

The  extent  from  1  to  1,25  will  reach  from  1,25  the 
depth,  to  1,56,=  the  contents  of  1  foot  in  length.  -Again, 
the  extent  from  1  to  1,56,  will  reach  from  the  length  = 
?1,75,  to  33,9  or  34,  nearly=the  solid  contents  in  feet. 

2.  Suppose  a  square  piece  of  timber  1,25  foot  wide,  and 
).56  foot  deep,  and  36  feet  long,  be  given,  to  tind  the  solid 
:ontents. 

Extend  from  1  to  7  ;  that  extent  will  reach  from  3S  to 
.5,2  =  the  solid  contents.  In  like  manner  may  the  contents 
of  Bales  be  found,  which  divided  by  40,  will  give  the  ton- 
nage. 

4.  The  Line  of  Sines,  (marked  SIN)  corresponding  to 
the  Logarithmick  Sines  of  the  degrees  of  the  Quadrant  be- 
gins at  the  let^t  hand,  and  is  numbered  towards  the  right  ; 
thus,  1,  2,  3,  4,  5,  6,  7,  8,  9,  10,  then  20,  30,  40,  ^c, 
ending  at  90°,  where  is  a  brass  centre  pin,  as  there  is  at 
'lie  ri^ht  hand  of  the  lines. 

5.  The  Line  of  Versed  Sines,  (marked  VS)  correspond- 
ing to  the  Log.  Versed  Sines  of  the  degrees  of  the  Quad- 
rant, begins  at  the  right  hand  against  90°  on  the  sine  ;  and 
Vom  thence  is  numbered  towards  the  left  hand  ;  thus,  10, 
.'0,  30,  and  40,  &c.  ending  at  the  left  band,  at  about  169°- 
iuach  of  the  subdivisions  from  10  to  30  is,  in  general  two 
degrees  ;  from  thence  to  90,  is  single  decrees  ;  from  thence 
10  the  end,  each  degree  is  divided  into  15  minutes. 

6.  The  line  of  Tangents,  (marked  TANG)  corresponding 
:o  the  Log.  Tangents  of  the  degree?  of  the  Quadrant,  be- 
^^ins  at  the  left  hand,  and  is  numbered  towards  the  right : 
thus,  1,  2,  3,  4,  and  so  on  to  10,20,30,  40  and  45,  where  is  a 
hrasspin  under  90°  on  the  Sines  ;  from  thence  it  is  numbered 
backwards  50,  60,  70,  GO,  6ic.  to  89,  ending  at  the  left  hand 


DESCRIPTION  AXD  USE  OF  THE  SECTOR.       IT 

where  it  begins  at  1  degree.  The  subdivisions  are  near- 
ly similar  to  those  of  the  Sines.  When  you  have  any  ex^ 
tent  in  your  dividers  to  be  set  off  from  any  numberless 
than  45°  on  the  line  of  Tangents  towards  the  right,  and  it 
is  found  to  reach  beyond  the  mark  of  45**,  you  must  see  how 
far  it  extends  beyond  that  mark,  and  set  it  off  tOTvards  the 
left,  and  mark  what  degree  it  falls  upon  ;  which  will  be  the 
number  sought,  and  must  exceed  45°.  If,  on  the  contrary, 
you  are  to  set  off  such  a  distance  to  the  right,  from  a  num- 
ber greater  than  45°,  you  must  proceed  as  before,  only  re- 
member, that  the  answer  will  be  less  than  45°,  and  you 
must  always  consider  the  degrees  above  45°,  as  if  they 
were  marked  on  the  continuation  of  the  line  to  the  right 
hand  of  45°. 

7.  The  line  of  the  Meridional  parts,  (marked  MER,) 
begin  at  the  right  hand,  and  is  numbered  thus,  10,  20,  30, 
to  the  left  hand,  where  it  ends  at  87** 

8.  This  line,  with  the  line  of  equal  parts,  (marked  EP) 
under  it,  are  used  together,  and  only  in  Mercator's  s;iiling. 
The  upper  line  contains  the  degrees  of  the  meridian,  or 
latitude  in  Mercator's  Chart,  correspondmg  to  the  de- 
grees of  longitude  on  the  lower  line.  The  use  of  this 
scale  in  solving  the  usual  Problems  of  Trigonometry,  plam 
sailing,  middle  latitude  sailing,  and  Mercator's  sailing,  will 
be  given  in  the  course  of  this  work  ;  but  it  will  be  u-ineces- 
sary  to  enter  into  an  explanation  of  its  use  in  calculating  the 
common  Problems  of  Nautical  Astronomy,  it  is  more  accu- 
rate to  perform  by  Logarithms. 

DESCRIPTION  AND  USE  OF  THE 
SECTOR. 

This  instrument  consists  of  two  rules  or  legs,  represent- 
ing the  radius,  moveable  round  an  axis  or  j«iiDt,  the  mid- 
dle of  which,  represents  the  centre,  from  whence  several 
scales  are  drawn  on  the  faces  ;  some  of  the  scales  are  sin- 
gle, others  double.  The  single  scales  are  like  those  on  a 
common  Gunter's  scale  ;  the  double  scales  are  those  that 
proceed  from  the  centre  ;  each  of  these  being  laid  twice 
on  the  same  face  of  the  instrument  viz.  once  on'each  leg. 
From  these  scales  dimen::ions  or  distances  are  to  be  taken 

B2 


18      DESCRIPTION  AXD  USE  OF  THE  SECTOR. 

when  the  legs  of  the  instrument  are  set  in  an  angular  posi- 
tion. The  single  scales  being  used  exactl}'  like  Gunter's 
scale,  1  shall  proceed  to  enuaierate  a  few  of  the  use*^  of  the 
double  scales,  the  number  of  which  is  seven  ;  viz.  the 
scale  of  lines,  (marked  LIX  or  L.)  The  scales  of  chords, 
(marked  CHO  or  C.)  1  he  scale  of  sines,  (marked  SIX  or 
S.)  The  scale  of  tangents,  to  43^  and  another  scale  of 
tangents,  from  45*^  to  about  76^  both  of  which  are 
marked  TAN  or  T.  The  scale  of  secants,  (marked  SEC 
or  S.)  And  the  scale  of  polygons,  (marked  POL.)  The 
scale  of  lines,  chords,  sines  and  tangents,  urider  45'^  are  all 
of  the  same  radius,  brginning  at  the  centre  of  the  instru- 
ment, and  terminating  near  the  other  extremity  of  each  leg, 
viz.  the  lines  at  the  division  10;  the  chord  at  60°  ; 
the  sine  at  90°  ;  and  the  tangents  at  45°.  The  re- 
mainder of  the  tangents,  or  those  above  45°  are  other 
:?cales,  beginning  at  a  quarter  of  the  length  of  the  former, 
counting  from  the  centre,  where  they  are  marked  with 
15°,  and  extend  to  about  76°.  The  secants  also  begin 
at  the  same  distance  from  the  centre,  where  they  are  mar- 
ked with  0,  and  are  thence  continued  to  75  Jeg.  The 
scales  of  polygons  are  set  near  the  inner  edge  of  the  legs, 
and  where  these  scales  begin,  they  are  marked  4  ;  and 
from  thence  are  numbered  backwards,  on  towards  ttie  cen- 
tre 12.  In  describing  the  use  of  the  Sector^  the  terms 
Lateral  Distance,  and  Transverse  Distance,  often  occur. 

By  the  former  is  meant  the  distance  taken  with  the  com- 
passes on  one  of  the  scales  ooly,  beginning  at  the  centre  of 
•he  sector.  By  the  latter  is  meant  the  distance  taken  be- 
tween any  two  corresponding  divisions  of  the  scales  of  the 
same  name,  the  legs  of  the  sector  being  in  an  angular  posi- 
tion. The  use  of  the  sector  depends  upon  the  propor- 
tionability  of  the  corresponding  sides  of  similar  triangles; 
demonstrated  in  Art.  53  Geometry.  For,  if  in  the  triangle 
ABC  we  take  AB=AC  and  AD=AE,  and  draw  DE  and 
BC,  it  is  evident  that  DE  and  BC,  will  be  parallel. — 
Therefore,  by  the  above  mentioned  proposition  AB;BC  :  : 
AD  :  DE  ;  so,  whatsoever  part  AD  is  of  AB,  the  same  part 
DE  will  be  of  BC  ;  hence  if  DE  be  the  chord,  sine  or 
tangent  of  any  arch  to  the  radius  AD,  so  BC  will  be  the 
Scin^  to  the  radius  AB. 

I'he  line,  of  Uaes,  is  useful  to  divide  a  given  lite  in- 


DESCRIPTION  AXD  USE  OF  THE  SECTOR.      19 


to  any  number  of  equal 
parts,  or  in  any  proportion, 
or  to  find  the  3d  and  4th 
proportionals, or  to  increase 
a  given  line  in  any  propor- 
tion. 

EXAMPLES. 

1.  To  divide  a  given  line 
into  any  number  of  equal 
parts,  as,  suppose  9.  Make  the  length  of  the  given  line,  a 
transverse  distance  to  9,  and  9  the  number  of  parts  pro- 
posed ;  then  will  the  transverse  distance  of  1  and  1,  be 
one  of  the  pirts,  or  ^  part  of  the  whole  ;  and  the  trans- 
verse distance  of  2  and  2,  will  be  two  of  the  equal  parts, 
or -I  of  the  whole  line,  kc. 

2.  Ifa  man  should  travel  52  miles  in  8  hours,  .how  far 
would  he  travel  in  3  hours  at  the  same  rate  ?         f 

Take  52  in  your  compasses  as  a  transverse  distance,  and 
set  off  from  8  to  8,  then  the  transverse  distance  3  and  3,  being 
measured  laterally,  will  be  found  equal  to  19-i-,  which  is 
the  number  of  miles  required. 

3.  Having  a  chart,  constructed  upon  a  scale  of  6  miles 
t©  an  inch,  it  is  required  to  open  the  sector,  so  that  a  cor- 
responding scale  may  be  taken  from  the  line  of  sines. — 
Make  the  transverse  distance  6  and  6,  equal  to  the  lateral 
distance  3  and  3  ;  then  set  off  any  distance  from  the  chart 
laterally,  and  the  corresponding  transverse  distance,  will 
be  the  reduced  distance  required. 

4  One  side  of  any  triangle  being  given  of  any  length; 
to  measure  the  other  two  sides,  on  the  same  scale. 

Suppose  the  side  AB,  of  the  triangle  ABC,  measure  50, 
what  are  the  measures  of  the  other  two  sides  2 

See  fig.  Take  AB  in  your 


dividers,  apply  it  transverse- 
ly to  50  and  50,  to  this  open- 
ing of  the  sector,  apply  the 
distance  AC  in  your  com- 
passes to  the  same  number 
on  both  sides  of  the  rule, 
transversely  ;  and  where  the 
two  points  fall,  will  be  the 
measure  on  the  line  of  hnes, 


B 


20 


USE  OF  THE  LL\E  OF  SIXES,  i-c. 


the  distance  required  ;  the  distance  AC,  will  fall  against 
63  and  63,  and  BC  against  45  and  45  on  the  line  of  lines. 
The  line  of  chords  oo  the  sector  is  very  useful  for  pro- 
tracting any  angle,  when  the  paper  is  so  small,  that  an  arch 
cannot  be  drawn  upon  it  with  the  radius  of  a  common  line 
of  chords.  Suppose  it  was  requiretJ  to  set  off  an  arch  of 
30^,  from  the  point  C,  of  the  small  circle  ABC  ;  take  the 
radius  in  your  compasses,  and  set  it  off  transversely,  Trom 
60°  to  60°  on  the  line  of  chords.  Then  take  the  transe- 
Terse  extent  from  30°  to  30°  on  the  chords  ;  and  place 
one  foot  of  the  compasses  at  C,  the  other  will  reach  to  E 
and  CE  will  be  the  arch  required.  By  the  converse  ope- 
ration, any  angle  or  arch,  may  be  measured  ;  with  any  ra- 
dius describe  an  arch  about  the  aii2:ular  point  :  set  that  ra- 
dius transversely  from  60°  to  60°.  Then  take  the  dis- 
tance of  the  arch,  intercepted  between  the  two  legs,  and 
apply  it  transversely  to  the  chords,  and  it  will  shew  the 


degrees  of  the  given  angle. 


.Vo<«.  When  the  angle  to  be 
protracted  exceeds  60'-'',  you 
must  lay  off  60°  ;  and  then  the 
remaining  parts  ;  or  if  it  be  a- 
bove  120^\  lay  off  C0°  twice; 
r.nd  then  the  remaining  parts. — 
In  this  way  any  arch  above  60° 
aay  be  measured. 


e 


USE  OF  THE  LINES  OF  SINES,  TAN- 
GENTS AND  SECANTS. 


By  the  several  lines  disposed  on  the  sector,  we  have 
scales  of  sevenil  r;£uii.     So  that, 

1.  Havi.iv  a  length  or  radius  given,  not  exceeding  the 
leigth  of  the  sector  when  opened,  v.e  cm  find  the  chord, 
sine,  6:c.  of  the  same.  Thus,  suppose  a  choid,  sine  or 
tan.  eTit  of  20°,  to  a  radius  of  2  incbt.>  be  required-  M.  ke 
2  in  ;->  the  transverse  opening  to  60  '  and  60°  on  the 
c'         :  then  will  ihe  same  extent  reach  from  15*^  to  45° 


USE  OF  THE  LLYES  OF  POLYGO.\'S,  21 

on  the  tangents,  and  from  90°  to  90°  on  the  sines,  so  that 
to  whatever  radius  the  line  of  chorcfe  is  set,  to  the  same  are 
all  the  others  set  also.  In  this  disposition,  therefore,  if 
the  transverse  distance  between  20°  and  20°  on  the 
chords  be  taken  with  the  compasses,  it  will  give  the  chord 
of  20°  ;  and  if  the  transverse  of  20**  and  20°,  be  in  like 
manner  taken  on  the  sines,  it  will  be  the  sine  of  20°  ;  and 
lustly  if  the  transverse  distance  of  20°  and  20°  be  taken 
on  the  tangents,  it  will  be  the  tangent  of  20°,  to  the  same 
radius  of  2  inches. 

2.  If  the  chord,  or  tangent  of  70°  were  required  ;  for 
the  chord  you  must  first  set  off  the  chord  of  60°,  or  the  ra- 
dius upon  the  arch,  and  then  set  off  the  chord  of  10°,  to 
tind  the  tangent  of  70°,  to  the  same  radius  the  scale  of  up- 
per tangents  must  be  used  ;  the  under  on«  only  reaching 
to  45°,  making,  therefore,  two  inches,  the  transverse  dis- 
tance 45°,  and  45°  at  the  beginning  of  thp  scale,  the  ex- 
tent between  70°,  and  70°  on  the  same,  will  be  the  tan- 
gent of  70°,  to  2  inches  radius. 

3.  To  find  the   secant  of  any  arch  ;  make  the  given  ra- 
dius the  transverse  distance   between  0,  and    0  on  the  se- 
cants;  then  will  the  transverse  distance    of  20°  and  20°, 
or  70°  and  70°,  give  the  secant  of  20°  or  70°  respective- 

4.  It  the  radius,  and  any  line  representing  a  sine,  tan- 
gent or  secant,  be  given  *,  the  degrees  corresponding  to 
that  line,  may  be  found  by  setting  the  sector  to  the 
given  radius,  according  as  a  sine,  tangent  or  secant  is  con- 
cerned ;  then  taking  the  given  line  between  the  compasses, 
and  applying  the  two  feet  transversely  to  the  proper  scale, 
and  sliding  the  feet  along  till  they  both  rest  on,  like  di- 
visions on  both  legs,  then  the  divisions  will  shew  the  de= 
grees,  and  parts  corresponding  to  the  given  line. 

USK  OF  THE  LINE  OF  POLYGONS. 

The  use  of  this  line  is  to  inscribe  a  regular  polygon  in  a 
circle.  For  example  ;  let  it  be  required  to  inscribe  an 
octagon  in  a  circle.  Open  the  sector,  till  the  transverse 
distance,  6  and  6  be  equals©  the  radius  of  the  circle  ;  then 
will  the  transverse  distance  of  8  and  8,  be  the  side  of  the 
inscribed  octagon,  or  polygoq, 


^2 

USE  OF  THE  SECTOR  LN  TRIGO- 
NOMETRY. 

AH  proportions  in  Trigonometry 
-ire  easily  wrought  by  the  double 
lines  on  the  sector ;  observing  that  the 
sides  of  triangles  are  taken  off  the  line 
of  lines,  and  the  angles  are  taken  off 
the  sines,  tangents  or  secants,  accord- 
ing to  the  nature  of  the  proportion. 
Thus,  in  the  triangle  ABC,  we  have 
given  AB  =  56,  AC  =  64,  and  the  angk  ABC  =  ^6°  30' to 
the  rest  in  this  case.  We  have  (by  art,  58  geometry) 
the  following  proportion  :  as  AC  (G4)  sine  of  the 
B  (46^  30')  :  :  AB  (56)  :  to  the  sine  of  the  angle  C,  and 
as  the  sine  B  :  is  to  the  side  AC  :  :  so  is  the  sine  A  :  to 
the  side  BC  ;  therefore  to  work  these  proportions  by  the 
sector,  take  the  lateral  distaace  64  =  AC  from  the  line  of 
lines,  and  open  the  sector  to  make  this  a  transverse  dis- 
tance of  46°  30'  =  angle  B  on  the  sines  ;  then  take,  the 
lateral  distance  56  =  AB  on  the  line  of  lines,  and  apply  it 
transversely  on  the  sines,  which  will  give  39°  24'  =  to  C  ; 
hence  the  sum  of  the  angles  B  and  C  is  53°  54'  which 
taken  from  180°,  leaves  the  angle  A  =  94°  6',  th^n  to 
work  the  secant  proportion,  the  sector  being  set  at  the 
^same  opening  as  before,  take  the  transeverse  distance  of 
94°  6'  =  the  angle  A  on  the  sines,  or  which  is  the  same 
thing,  the  transeverse  distance  of  its  supplement  85°  54'  ; 
then  this  applied  laterally  to  the  lines,  gives  the  side  sought 
BC  =88.  In  the  same  manner  we  might  solve  any  prob- 
lem in  trigonometry,  with  the  tangents  and  secants,  in- 
stead of  measuring  them  on  the  sines,  as  in  the  preceeding 
example. 

All  the  problems  that  occur  in  mutlcal  astronomy,  may 
be  solved  by  the  sector  ;  but  the  calculations  by  logarithms 
are  much  more  accurate. 

THE  SLroiNG  RULE 

Consists  f  f  a  fixed  part  and  a  slider,  and  is  of  the  same 
diaieojions  as  a  common  Gunter's  scale  :  and  has  the  same 


THE  SLIDIKG  RULE.  23 

lines  marked  on  the  fixed  part,  as  that  scale  ha?,  and  also  on 
the  plain  scale  ;  and  these  lines  may  be  used  with  a  pair 
of  compasses, in  the  same  manner,  as  the  lines  of  those 
scales. 

As  a  description  of  those  lines,  has  already  been  given, 
it  will  be  unnecessary  to  repeat  it  here  :  It  being  sufficient 
to  observe,  that  there  are  two  lines  of  numbers,  viz  >•  a 
line  of  Logarithmick  sines,  and  a  line  of  Logarithmick  tan- 
gents on  the  shder.  And  the  slider  may  be  shifted,  so  as 
to  lix  either  face  of  it  on  either  side  of  ihe  tixed  part  of  ihe 
•cale. according  to  the  nature  of  the  question  to  be  solved. 

In  solving  any  problem  in  Arithmetick,  Trigonometry, 
plam  sailiug  &c.  let  the  pro-portion  be  so  stated,  that  the 
first  and  thiid  terms  may  be  alike,  and  of  course,  the  second 
-and  fourth  terms  will  be  alike.  Then  bring  (he  tirst  term 
of  the  analogy  on  the  fixed  part,  against  the  second  term 
on  the  slider  ^  and  against  the  third  term  on  the  fixed  part, 
will  be  found  the  fourth  term  on  the  slider.  Or  if  neces- 
sary, the  first  and  third  terras  may  be  found  on  the  slider, 
and  the  second  and  tborih  on  tl-e  fixed  part.  Multiplica- 
tion and  Division  are  performed  by  this  rule  or  method  ; 
only  consider  unity  as  one  of  the  terms  of  the  analogy, 

MULTIPLICATION  BY  THE  SLIDING  P.ULE. 

To  perform  multiplication,  set  I  on  the  line  of  num- 
bers of  the  fixed  part,  against  one  of  the  factors  on  the  line 
of  numbers  on  the  slider  ;  then  against  the  other  factor  on 
the  fixed  part  will  be  found  the  product  on  the  slider. 

JVoie.  if  the  first  and  second  terms  are  alike,  or  of  one 
name,  instead  of  the  first  and  thin!,  you  must  bring  the 
first  term  on  the  slider,  against  the  thirJ  on  the  fixed  part, 
and  against  tl:re  second  term  on  the  slider,  will  be  found  the 
fourth  term  oa  the  fixed  part  ;  or  if  necessary  the  first  and 
second  terms  may  be  found  on  the  fixei  part,  and  the  third 
and  fourth  on  the  slider. 

EXAMPLES. 

1.  To  find  the  product  of  5,  by  12.  Draw  out  the  slider, 
till  1  on  the  fixed  part,  coincides  with  5  on  the  slider  ;  then 
opposite  12  on  the  fixed  part,  will  be  found  60=:  the  pro- 
duct, on  the  slider. 


24  THE  SLIDLVG  RULE. 

2.  To  find  the  product  of  50,  by  1 2.     Not  moTins  the  sH 
der,  count  5  to  be   50  ;  count  12  a«  before  ;  then   opposite 
12  on  the  dxed  part,  will  be  found  600  on  the  slider. 

3.  Place  the  slicker  as  before,  count  5  to  be  500.  and  12  t« 
be  1200;  the  ansv^er,  600,000;  will  be  found  on  the 
slider. 

4.  To  find  the  product  of  17  hy  25.  Draw  out  (he  slider 
till  1  on  the  fixed  part,  coincifies  with  17  on  the  slider,  then 
opposite  25  on  the  fixed  part,  will  be  found  425  on  the 
slider. 

5.  To  find  the  product  of  17  by  17.  Draw  out  the  slider, 
till  1  on  the  fixed  part  coincides  with  17  oo  the  «li«ler, 
then  opposite  17^on  the  fixed  part,  will  be  found  289  on 
the  slider. 

6.  Place  tne  slider  the  sanse  as  before  ;  against  60  on  the 
fixed  part  will  he  found  850  on  the  slider. 

7.  The  slider  laying  at  17  as  before,  count  50  or  5  to 
be  opposite  500  on  the  fixed  part,  w  ill  be  found  8500  on 
the  sli'.ier. 

8.  Place  the  slider  as  before,  count  17  to  be  1700,  count 
3  to  be  300  on  the  fixed  part,  then  opposite  300  on  the  fixed 
part  will  be  found  510,000  on  the  slider. 

9  To  find  the  product  of  2! 4-  by  20.  Draw  out  the 
slider  till  the  centre  1  on  the  tixed  part  coincides  with 
21i  on  the  slider,  then  opposite  20  on  the  fixed  part  will  be 
lauiid  430  on  the  slirler. 

10  To  find  the  |jroducl  of  5  by  2^  count  the  first  1  on 
the  fise^  p  irt.  to  bs  yV'  *^'^  centre  one  count  1,  draw  out 
the  slider  till  1  on  liie  fixed  part  coincides  with  5  on  the 
slider,  opposite  2^  on  the  fixed  part  will  be  found  15^  oh 
the  slider. 

DIVISION    BY    THE    SLIDING    Rl'LE. 

Place  the  divisor  on  the  line  of  numbers  of  the  fixed 
part  against  1  00  the  slider,  then  against  the  dividend  found 
90  the  fixed  part,  will  be  found  the  quotient  on  the  slider, 

BXA5tPLES 

1  To  divide  60  by  5.  Set  5  on  the  fixed  part  against  1 
on  the  slider,  then  agaiast  60  on  the  fixed  part,  will  be 
fouod  r2=the  quotient  00  the  slider. 


THE  SLIDLKG  rule. 


'     25 


2.  To  divide  400  by  27.  Set  27  on  the  fixed  part  against 
1  on  the  slider,  then  against  400  on  the  fixed  part,  will  be 
found  14|-f-  or  about  H^  on  the  slider. 

3.  To  answer  several  questions,  not  moving  the  slider  in 
in  one  lesson,  the  slider  placed  as  in  Exanaple  2. 


Div 


You  will  have 
gone  the  length 
of  the  fixed  part 
to  A,  on  the  state- 
ment. 


isors. 

Dividends. 

27 

-:-     400 

27 

-:-     600 

27 

-:-     600 

27 

-:-     700 

27 

>:-     800 

27 

-;-     850 

27 

-:-     900 

27 

-:-  1000 

Qnotients. 


112  2 


or 


Ui 


18-i^or  184- 


^2  I- 


2 

9.^ 


or  ii,- 
25|4-  or  26  nearly 


29-1^  or  2P2 
Si-^-f  or  31^ 
33^ 
37^V  Of  37 


4.  To,divide  any  nnmber  from  700  to  6000  that  is  at  B  on 
the  s^lider,  the  full  of  the  extent  of  the  slider.  From  the 
statement,  dr<-.w  out  the  slider  on  A,  to  the  left  hand  of 
the  centre  1,  to  the  figure  6,  representing  60  on  the  fixed 
part,  over  I  on  the  slider  ;  then  against  7  representing  700, 
on  the  fiXed  par',  will  be  found  11-|  on  the  slider.  Now, 
not  moving  the  slider,  you  may  find  this  lesson  from  700  to 
6000. 


ivisors.     Di^ 

V'idends. 

Qtiotients. 

60       - 

:-     700 

1^4 

60       - 

:-     800 

13^' 

60       - 

-     900 

15 

60       - 

-   1000 

16-2 

60       - 

-  2000 

33i    Ending    at 

60       - 

-  3000 

50      B,    at    the 

60       - 

-  4000 

6e|.   right  hand 

60       - 

-  5000 

8c  1     of  the  >ii^ 

60       -. 

-  6000 

100      der. 

EXAMPLES    IX    THE    RULE    OF    THREE    BY    THE 
SLIDING    RULE. 

If  3  lbs.  of  beef  cost  21  cents,  what  will,  from  30  to  100 
lbs.  cost? 

C 


2C  THE  SLIDLXG  RULE. 

This  lesson  reaches  from  30  to  70  diflerent  statement?, 
viz.  from  50  to  100,  not  moving  the  slider  ;  bring  3  on  tlio 
letter  A,  of  the  fixed  part,  on  the  line  of  numbers  against 
21  on  the  Hne  marked  B,  on  the  shder  ;  then  against  30 
on  the  fixed  part  on  A,  will  be  found  on  the  slider,  $2,10  ; 
and  against  35  lbs.  will  be  2,43  ;  40—2,80  ;  50—3,50, 
60—4,20;   75—5,25;   90—6,30;    100—7,00. 

2.  If  4-1- yds.  cost  g23,  what  will  20  yds.  cost  ? 

RULE. 

Draw  out  the  slider,  till  §23  coincides  with  41-  on  the 
fixed  part  ;  then  against  20  on  the  fixed  part,  will  be 
found  ^102,  on  the  slider.  Now  not  moving  the  slider, 
at  A,  on  the  fixed  part,  100  yds.  will  be  found  to  the  an- 
swer on  the  slider  ==§5,11. 

3.  If  4  lbs.  of  sugar  cost  §l,50,what  will  20  lbs.  cost? 
Bring  4  on  the  line  of  numbers  on  the  fixed  part,  against 

gl,50onthe  line  of  numbers  on  the  slider  ;  then  against 
20  on  the  line  of  numbers,  on  the  fixed  part,  will  be  found 
§7,50  on  the  slider.  Now  not  moving  the  slider,  against 
40,  on  A,  will  be  found  §15,00  on  the  slider.  Again,  not 
moving  the  «lider,  against  80,  on  A,  will  be  found  §30,00  ; 
and  at^A,  100  lb?  on  the  slider,  B  will  be  found  §37,50 — 
ABCD  on  the  right  of  the  rule. 

4.  To  find  the  circumference  of  a  circle,  wbose  diame- 
ter shaU  be  20. 

RULE. 

Draw  out  the  slider,  till  22  on  the  slider  coincides  with 
7  on  the  fixed  part,  then  against  20  on  the  fixed  part,  will 
be  found  6:4.  or  Gt'^  on  the  slider.  Again,  not  moving  the 
slider,  against  25  on  the  fixed  part,  will  be  found  7?^-  on 
the  slider.  Again,  not  movins:  the  slider,  against  40  on  the 
fixed  part,  will  be  found  IScf  on  the  slider.  Again,  not 
moving  the  slider,  against  60  on  the  fixed  part,  will  be 
found  \V>i^  on  the  slider.  Now,  not  moving  the  slider,  a- 
gainst  100  at  A,  on  the  fixed  part,  will  be  found  314-f  on 
tie  slider. 

5.  If  one  yard  of  cloth  cost  §9,00,  what  wdl  ^  of 
a  V'frd  cost  ? 

'Draw  out  the  slider,  till  9  on  the  slider  coincides  with 
10  on  the  fixed  part,  then  against  5  on  the  fixed  part,  will 
oe  fo«nd  on  the  slider  §2,83. 


THE  SLIDING  RULE. 


21 


BOARD  MEASURE  BY    THE  SLIDING   RULE. 
EXAMPLES. 

1.  To  measure  a  board  12  feet  long,  atid  12  inches 
wide  :  12  on  the  fixed  part,  to  the  right  of  the  centre  1 
counts  12  feet  in  length  ;  but  12  on  the  slider  give  12  to 
12,  or  12  i'eet 

2.  A  board  12  feet  lon^,  and  19  inches  wide. 

Draw  out  the  slider,  till  19  coincides  with  12  on  the  fix- 
ed part,  that  makes  the  board  19  feet=the  answer  on  the 
slider  ;   19  inches  the  answer  in  feet. 

3.  A  board  14  feet  long  and  20  inches  wide. 

Draw  out  the  slider  till  20  coincides  with  12  on  the  fix- 
ed part,  then  against  14  on  the  fixed  part,  the  answer  23-^ ft. 

4.  A  board  22  feet  long,  20  inches  wide. 

Draw  out  the  slider  till  20  inches  coincides  with  12  on 
the  fixed  part,  and  against  22  on  the  fixed  part,  will  be 
found  the  answer  361  feet  on  the  slider. 

5.  A  board  table  that  extends  fiom  4  to  100  feet  in 
length,  and  36  inches  wide. 

Draw  out  the  slider,  till  36  coincides  with  12  on  the  fix- 
ed part ;  count  the  1st  1  on  the  fixed  part  10  ;  begin  at  4 
on  the  fixed  part  4,  so  on  to  10  at  the  centre,  and  so  on  to 
100  on  the  right  hand,  to  A.  Begin  on  the  slider  at  4, 
and  reckon  at  different  lengths. 


28  THE  SLIDIXG  RULE. 

6.  A  log  14  feet  long  cuts  27  board?,  each  board  36 
.iicbes  wide,  how  many  feet  in  one  board  ? 

Ans,  4-2  feet. 

J  low  many  feet  in  the  27  boards  ? 

Draw  the  slider  till   27   coincides   with  the  centre   1,  a- 
gninst  42   on   the  tised  pari,  will  be  the  an=wer  on  the  sli- 
;cr=to  1 134. 

A  log  12  feet  long,  24  inches  in  diameter,  cuts  15  boards, 
?0  inches  broad. 

Draw  out  the  slider,  till  20  is  agrdnst  12  :  20  will  be  the 
answer  for  one  board.  Draw  out  the  slider  till  15  comes 
against  the  centre  1  on  the  fixed  part,  and  against  20  on 
the  fixed  part  will  be  found  300  on  the  slider=the  answer 
in  board  measure. 

A  log  2  feet  in  diameter,  and  under  :  2  inches  on  each 
side  are  allowed  for  «lab,  and  4-  for  saw  calf,  and  1  board  for 
wane  :  and  from  24  to  36  inches  diameter,  3  inches  for 
>lab,  ^  for  saw  calf,  and  2  boards  for  wane. 

A  log  28  inches  at  the  small  end,  will  cut  13  boards,  on- 
jy  16  measured. 

Draw  out  the  slider  till  22=th«  breadth  of  the  board, 
comes  against  12,  and  against  14  =the  length  on  the  fixed 
part,  will  be  found  the  answer  on  the  slider  tor  one  board 
=254-.  Now  draw  out  the  slider  till  16,  the  number  of 
hoards,  comes  against  the  centre  1  :  novv  to  find  the  rest, 
say  the  log  was  14  feet  long,  your  answer  Qn  the  slider  is 
414  feet  nearly. 

Again,  a  log  14  feet  long.  36  inches  at  the  small  end  slab- 
)ed,  leaves  the  board  30  inches  wide,  i  tor  sawcalf,  leaves 
24  and  2  wane  leaves  22.  Draw  out  the  slider  till  30 
comes  against  12  on  the  fixed  part,  and  under  14  on  the 
fixed  part,  vvill  be  found  35  on  the  slider.  Then  draw  out 
the  slider  till  22  comes  a^inst  the  centre  1,  and  against 
35  will  be  lound  770  on  the  slider,  which  will  he  the  an- 
swer tor  a  log  36  inches  in  diameter,  and  14  feet  long. 

A  log  20  inches  at  the  small  end,  and  16  feet  long,  cuts 
13  boards  that  are  16  inches  wide,  and  but  12  measured, 
bow  many  teet  ?  An?.  255 

A  log  i6  inches  in  diameter.  14  feet  long,  cuts  9  boards, 
and  but  8  measured,  how  many  feet?  Answer  112  fee- 
on  the  slider. 


THE  SLIDIXG  RULE. 


29 


TO    MEASURE    SQUARE    TIMBER    IN    SOLID    FEET    BY 
THE    SLIDING    RULE. 


To  measure  a  stick  of  timber  60  feet  long^ 


RULE. 

Draw  out  the  slider  to  the  left  hand,  till  the  length  of  the 
timber  found  on  the  slider,  shall  correspond  to  12  on  the 
girt  line  ;  then  against  the  mches,  the  stick  is  square  on  the 
girt  line,  will  be  found  the  number  of  cubic  feet  on  the  sli- 
der. 

EXAMPLE. 

and  from  5  to  40  inches  square. 

Draw  the  slider  to  the  left  hand,  till  6  on  the  slider 
(which  call  60,)  corresponds  with  12  on  the  girt  line, 
and  against  6  on  the  slider,  will  be  found  10^^^^  on  the 
girt  line.  The  same  answer  can  be  found  by  drawing  the 
slider  to  to  the  right,  but  the  divisions  are  not  so  easily 
distinguished,  without  more  practice. 

By  letting  the  slider  remain,  you  may  solve  all  the  ques- 
tions proposed  above  in  a  short  time,  and  will  put  their 
answers  m  a  table  for  exercise. 


laches 

Cubic  feet 

laches 

Cubic  feet 

hiches 

Cubic  feet 

-«_• 

sqr. 

in  the  slick. 

sqr. 

in  the  stick. 

s.jr. 

in  the  stick. 

0) 

r1> 

5 

10,42 

14 

82 

23 

220 

C 

6 

7 

15 

20,42 

iH 

15 

88 
94 

23^ 
24 

2311 
242 

"ra 

71 

23i 

log 

lOOl 

24i 

250 

w.< 

8 

261 

16 

106^ 

25 

260 

^h 

30tV 

17 

120^ 

26 

282^ 

-s 

9 

33^ 

18 

135 

27 

303 

■^j 

H 

371 

181 

142 

28 

327 

.a 

10 

41f 

i    19 

150 

29 

352 

Q 

i   10^ 

46 

19^ 

158- 

30 

o  to 

11 

50,42 

::o 

166* 

31 

402 

en 

111 

1   12 

1   12| 
i   13 

55 
60 
65i 
7Cf 

2ui 
2(J| 
21 

22 

ICO 

184| 
202 

32     ] 
35 
38 
40 

426 
510 
602 
667  nea 

-a 

c 
•-I 

C3 


30  THE  SLIDLYG  RULE. 

TO    MEASURE    HEWN    TIMBER    THAT    IS    NOT 
SQUARE,    BY    THE    SLIDNG    RULE. 


EXAMPLES. 

i.  To  Iind  the  solid  feet  in  a  stick  of  limber,  50  feet  m 
lengthy  and  7  by  10  inches. 

Draw  out  the  slider,  till  50  coincides  with  12  on  the  grirt 
line,  and  against  the  thickness,  7  inches,  founfl  on  the  girt 
line30u  will  find  17  on  the  slider,  whioh  is  the  answer,  at 
7  inches  square.  There  will  then  remain  3  times  7=21 
inches,  and  50  (eci  long,  yet  to  find  ;  to  obtain  whicli,  draw 
(he  slider  to  the  right,  till  21  on  the  slider  coincides  with 
12  on  the  line  marked  A  ;  then  against,  50,  the  length 
found  on  A,  you  will  find  ol~  on  the  slider  ;  this  must  be 
divided  by  12  and  it  will  give  7  feet  ?~,  inches  or  '<i,  which 
being  added  to  the  17,  before  found,  gives  24^  feet,  con- 
tained in  the  stick. 

2.  To  find  the  solid  feet  in  a  stick  45  feet  long,  27  inch- 
es wide,  and  22  inches  thick. 

;  "Dravv  out  the  slider,  till  45  on  the  slider  coincides  with 
12  on  the  girt  line,  then  over  22,  found  on  the  girt  line, 
will  be  151|-  on  the  slider,  which  gives  the  dimensions  of 
a  stick  45  feet  long  and  22  inches  square.  Now  5X22  re- 
main=  1 10,  which  number  find  on  the  slider,  and  let  it  co- 
incide with  12  on  A  ;  then  against  45  on  A,  you  will  find 
413  on  the  slider  ;  this  divided  by  12  gives  34^  which  ad- 
ded to  151-1  before  found,  gives  186  nearly,  for  the  an- 
swer. 

3.  To  fmd  the  solid  feet  in  a  stick  of  timber,  GO  feet 
long,  30  inches  wide  and  14  inches  thick. 

Draw  out  the  slider,  till  60  on  the  slider,  comcldes  with 
12  on  the  girt  line,  then  over  14  on  the  girt  line,  jou  will 
i.\i  I  Clf  OQ  tlie  slider  ;  now  by  doubling  this,  will  give  the 
•contents,  equal  to  28  bv  14,  and  the  2  left  is  2  by  14, 
which  is  -f  of  14;  divide  8l4  =  n|-;  then  add  81|  81|. 
11  9.  =  !  75  the  answer.  Or  find  the  avarage  square=20,5. 
Then  find  20,5  on  the  girt  line,  and  directly  over  it  on  the 
Slider  will  be  175  ;  observing  to  draw  out  the  slider,  till 
the  length  of  the  stick  in  feet  coincides  with  12  on  the  girt 
line. 


THE  SLWmG  RULE,  31 

4.  To  find  the  solid  feet  ofa  stick  of  timber,  55  feet  long, 
25  inches  wide  and  20  thick. 

Draw  out  theMider,  till  55  coincides  with  12  as  before  ; 
then  over  20,  found  on  the  girt  line,  will  be  153  nearly  ; 
this  divided  by  4,  and  the  quotient  added  gives  19H  feet 
the  answer.  Or  for  the  5  inches  left,  say  5  times  20  i3= 
100  ;  the  square  root  of  which  is  10  :  now  look  on  the  sli- 
der over  10,  will  be  found  38^  as  before. 

A  little  practice  will  render  the  performance  easy  and 
expeditious. 

Where  it  is  practicable,  cast  it  into  a  square  ;  as  9  by  4, 
multiplied,  gives  33,  the  square  root  of  which  is=  6  the 
answer.  Or  cast  the  log  into  board  measure,  by  drawing 
the  slider  against  30,  the  width,  on  the  slider  under  12  on 
the  fixed  part  A  ;  then  under  60,  the  length  on  the  fixed 
part,  you  will  find  150  on  the  slider,=number  of  square 
feet  in  one  board  ;  then  lay  14,  the  width  on  the  slider, 
under  1  on  the  fixed  part,  then  against  150  on  the  fixed 
part,  will  give  2100  feet  of  boards  on  the  slider;  now  di- 
vide by  12  by  drawing  1  on  the  slider,  against  12  on  the 
fixed  part,  then  againsf  2100  on  the  fixed  part  will  be  found 
]  75  on  the  slider,  the  answer  in  cubic  feet. 

GUAGIXG    OF    ROUND  TIMBER,  OR  TAKING  A    GUAGE 
POINT,  AND  CASTING  INTO  CUBIC  FEET. 

RULE.  Let  your  guage  point,  found  on  the  girt  line  be 
13,54  inches  ;  now  to  find  the  contents  of  a  stick  or  log, 
bring  the  length  of  the  timber,  found  on  the  slider,  to  coin- 
cide with  the  above  guage  point;  then  the  diameter  in 
inches  or  parts,  found  on  the  girt  line,  will  coincide  with 
the  number  of  cubic  feet  on  the  slider. 

EXAMPLE.  Suppose  a  stick  of  timber  12  feet  long,  and  15 
inches  in  diameter  ;  how  many  cubic  feet  ? 


Against  15  inches,  will  be  found  15  (eei, 

5|  *' 


20       "  "  •'     26-2 


i<       3Q      tt  i<  «•     59     '< 

f.       35      u         «i  «    30,8  " 


32 


measuhatio.y. 
MENSURATION. 


PROBLEM    I. 


To  find  the  Area  of  a  Triangle. 

Multiply  the  base  by  half  the  perpendicular;  or  multi- 
ply half  the  base  by  the  whole  perpendicular,  and  the 
product  will  be  the  area  required. 


EXAMPLE.     Given  AC,  the  base  =30 
feet,   and    the   perpnedicular  BD=20. 
30=  base.     *  15=  half  base. 

10  =  halfperp.  20  =  perp. 

300  =  area.  300  =  area. 


PROBLEM    II. 

To  find  the  Area  of  a  Circle.* 

Square  the  diameter  of  the  circle,  and  multiply  that 
square  by  the  decimal  ,7854,  which  deciinU,  is  as  much 
less  than  unity  or  1 ,  as  the  inscribed  circle  is  to  its  super- 
scribing square.  Or  which  is  nearly  the  saaie,  multiply 
the  squa»e  by  1 1  and  divide  by  14. 


*  The  oircuruference  of  anv  circle  mav  be  fo'ind,  by  multiplying 
the  diameter  by  i2  and  dividing  that  product  by  7,  or  multiplying^ 
the  diameter  by  355  and  dividing  by  113,  which  numbers  may  be 
easily  remembered,  by  observing,  that  the  two  numbers  bein^  set 
together,  thus,  113,355  make  a  double  series  of  odd  numbers  viz. 
11,33  and  55.  The  circumference  of  any  circle  bein^  griven,  the 
diameter  may  be  found,  by  reversing  the  above  rule.  Thus,  multi- 
ply the  circumfarence  by  7  and  divide  by  22.  or  better,  m^^ltiply  by 
113  and  divide  by  355.  Or  you  may  divide  the  c-rcamiereioe  by 
S:1416,  or  to  fiud  '.he  circuml'^rence,  multipiy  the  diameter  by  3,1416. 


MEXSURATIOX. 
EXAMPLE.     A  circle  whose  diameter  DB  =  10,6. 


33 


10,6 
10,6 

636 
106. 


112,36=  square. 
11 


14)  1235,96  (88,282 
112 


112,36  =sqare. 
,7854 


115 
112 


44944 
68180 
89888 
78652 


39 
28 


116 
112 


88,247544=  area. 


40 

PROBLEM    III. 


To  find  the  Area  of  an  Ellipsis,  or  Oval. 

Multiply  the  longest  or  transverse  diameter,  by  the 
bhortest  or  conjugate  diameter,  and  this  product  by  ,7854, 
5md  the  last  product  will  be  the  area. 


EXAMPLE.     Suppose    the    transvesre 
AC  =  12  and  the  conjugate  BD  =  10 
12 
10 


120 

,7854 


94,2480  area 


34 


MEA'SURATIOjY. 


Definition.  A  sector  of  a  circle  is  a 
part  of  I  circle  bounderl  b)  two  radii, 
or  seu)idiameters,  and  bj  an  arch  of 
Ihe  primitive  circle  whose  area  m:\y 
be  found  by  means  of  the  whole  area 
of  the  whole  circk;  Thus,  as  360 
degrees,  i??  to  angle  or  degrees  be- 
tween the  two  legs  or  radii  of  the 
sector,  so  is  the  area  of  the  whole 
circle,  to  the  area  of  the  sector. 


Sector. 


area. 


EXAMPLE.  As  360**  '.  288^  :  :  314,16  :  261,328**  the  Ads. 


PROBLEM  IV. 


Tojlnd  the  Solidity  of  a  Cylinder. 

Multiply  the  square  of  the  diameter  of  either  end  or 
base  by  ,7854  which  will  give  the  area  of  the  base  ;  then 
multiply  this  area  by  the  length  and  it  will  give  the  solidiljy 
required. 


Cylinder. 
13 


B 


EXAMPLE.  AD  or  BC=5 

6 


D  13  C 

25=  square  of  the  diameter  of 
,7854      the  base  or  end. 

100 
125 
200 
175 

19,6350  =  area  of  the  base  or  end. 
13 

68905 
19635 


25,5255  =  solidity  of  the  cylinder  in 

ieet. 


MEjXSURATIOX.  35 

problem  v. 

To  find  the  Solidity  of  a'Grindstone, 

Grindstones  in  the  form  of  cj/linders,  are  sold  by  the 
stone  of  24  inches  diameter  and  4  inches  thick  :  Now,  to 
know  how  many  such  stones  are  contained  in  a  given  cylin- 
der, multiply  the  square  of  the  diameter,  in  inches,  by  the 
thickness,  m  inches,  and  divide  the  product  by  2304  and 
you  will  have  the  number  required. 

EXAMPLE 

How  many  stones  of  24  inches  diameter  and  4  thick,  are 
contained  in  a  stone  of  36  inches  diamefer  and  8  inches 
thick  ? 

36  inches  diameter. 
36 


216 
108 


1296  = square. 
8  =  thickness. 


2304)  10368  (4,5  Ans.  =4  I -2  stones. 
9216 


11520 
11520 


This  problem  may  be  solved  rery  expeditiously,  by 
means  of  the  line  of  numbers  on  Guntej-'i  scale,  by  the  fol- 
lowing rule.  Extend  from  48  to  the  diameter  :  continue 
that  extent  three  times  its  length,  from  the  thickness,  and 
it  will  reach  to  the  number  of  stones  required  So  in  the 
foregoing  example,  extend  from  48  to  36  the  diameter  : 
continue  that  esten)  three  times  its  length,  from  the  thick- 
ness, which  is  8  inches,  and  it  will  reach  to  4,5  or  4  1-2  the 
answer. 


36 


ME.YSUIL1TI0\. 


PROSLLM    VI. 

Tojind  the  Solidity  of  a  Pyramid  or  Cone^ 

First  find  the  area  of  the  base,  whether  square,  triansfu- 
lar  or  circular,  or  any  other  form,  by  the  proper  rule  for 
each  ;  then  muhiply  this  area  by  one  third  the  perpendicu- 
lar height,  and  it  will  give  the  solidity  required. 

F.XAEPLES. 

1.  What  i?  the  solidity  of  a  pyramid  which  has  a  square 
bsse,  \yhose  side  is  4  feet, and  perpendicular  bight  6  feet. 


4 
4 

1-6  =  area 
2  =  i  height. 

32  =r=  solidity. 


2.  What  is  the  solidity  of  a  cone  whose  base  is  10,6  feet^ 
and  perpendicular  height  i«  30  feet. 


10,6  =  diameter  of  the  base 
10,6 


112,36=  square. 
,7854 


88,247544  =area. 

10  =  ^  hei?ht.==50 


882,475440  =  soliditv. 
Thi«?  soliiiity   divided  by    40,   will  give  the 
number  of  tons  in  that  cone. 

4|0)  882,47544|0 


22,061 836  =  *or,« 


2d. 

h 


MENSURA  TlOy,  37 


FROBLEM    Vir. 


•     To  find  the  Tomiagc  of  a  Ship. 

By  a  law  of  Congress  of  the  United  States  of  America, 
•the  tonnage  of  a  ship  is  to  be  found  in  the  following  manner. 

"If  the  vessel  be  double  decked,  take  the  length  thereof, 
from  the  fore  part  of  the  main  stern  to  the  after  part  of  the 
stern  post  above  the  upper  deck  ;  the  breadth  thereof,  to 
be  taken  at  the  broadest  part  above  the  main  wale,  half  of 
which  breadth,  shall  be  accounted  the  depth  of  such  ves- 
sel ;  tvien  deduct  from  the  length  three  fifths  of  the  breadth, 
then  multiply  the  remaind-er  by  the  breadth  and  this  pro- 
duct by  the  d-epth,  divide  this  Jast  product  by  ninety -five,  arid 
tiie  quotient  will  be  the  ^rue  contents  or  tonnage  of  such 
vessel.  If  the  vessel  be  single  decked,  take  the  length  and 
breadth,  as  above  directed,  in  a  double  decked  vessel  ;  and 
deduct  from  the  length,  three  fifths  of  the  breadth;  and 
taking  the  depth  from  the  uwder  side  of  the  deck  plank  to 
the  ceiling  IB  the  hold  ;  then  multiply  and  divide  as  above 
directed,  and  the  quotient  will  be  the  true  contents  or  ton- 
nage of  such  vessel." 

EXAMPLE.     If  the  length  ef*  a  double  decked  vessel,  be 
80  feet,  and  the  breadth  24  ie.e.\,  what  is  her  tonnage  ? 

V 

eoft.length  95)    18892,8  (198,871  Ans, 

14,4,  I  the  breadth.  95 


^5,6  939 

24  breadth.  865 


2624  842 

1312  7G0 


1574,4  828 

12  depth,  or  \  the  breadth.  760 


1^892,8  to  be  divided  bv  95.         680 

665 


150. 


n 


38  GU AGING. 

Note.  Ship  carpenters,  in  fint^ing  the  tonnage,  multiply 
the  length  of  the  keel,  by  the  breadth  of  the  main  beanr>, 
and  the  depth  of  the  hold  in  feet,  and  then  divide  the  pro- 
duct by  95  ;  the  quotient  is  the  number  of  tons.  In  double 
decked  vessels,  half  the  breadth  is  taken  for  the  depth 

GUAGING  OF  CASKS. 

Having  found  the  number  of  cubic  inches  in  any  body, 
by  the  preceding  rules,  you  may  from  thenre,  determine 
their  contents,  in  gallons,  bushels,  he.  by  dividing  that 
number  of  cubic  inches,  by  the  number  of  cubic  inches  in 
a  gallon,  bushel,  &c.  respectively.  A  wine  gallon,  by 
which  most  liquors  are  measured,  contains  231  cubic  inch- 
es. AJ?eer,  ale,  or  milk  gallon,  contains  282  cubic  inch- 
es, ^bushel  of  corn,  malt,  fiic.  contains  2150,4  cubic 
inches.  This  measure  is  subdivided  into  8  gallons  ;  each 
of  which  contains  268,8  cubic  inches.  In  all  the  following 
rules,  it  supposes  the  dimensions  of  a  cask  or  ressel,  to 
be  given  in  inches,  and  decimal  parts  of  an  inch. 

PROBLEM    I. 

To  find   the  number  of  Gallons  or  Bushels  in  a  Vessel  of  a 

Cubic  Form. 

Divide  the  cube  of  one  of  the  sides  in  inches  by  231, 
and  it  gives  wine  gallons,  divide  the  same  cube  by  282 
and  it  gives  beer  gallons  ;  and  divide  by  2150,4  and  it  gives 
the  number  of  bushels  the  vessel  will  hold. 

EXAMPLE.  Required  the  number  of  wine  and  beer  gal- 
lons, also  the  bushels  contained  in  a  cubic  box  or  cisterR 
whose  side  is  60  inches. 


QUAGL^V.  3i 


50 
50 

2500 
50 


B31)  125000  (541,1  gallons,  wine  measur^v 
1155 


950 
924 

260 
231 


290 
230 


;?82)  125000  (443,26  gallons,  beer  measur*, 
1128 


1220 
1128 


920 

846 

740 
664 

1760 

:/>lo0,4)  125000,0  (58,1  bushels. 
107520 


174800 
172032 


27680 


-4d  CUAGLXa. 

PROBLEM    II. 

To  find  the  number  of  Gallons  or  Bushels  contained  in  a  body 
of  a  Cylindrical  Form, 

Multiply  the  square  of  the  diameter  of  either  end  or  base, 
ly  the  length  of  the  cylinder,  and  divide  the  product  by 
294,12  and  the  quotient  vviH  be  the  number  of  wine  gal- 
lons divide  the  same  number  by  359,05  the  quo- 
tient will  be  the  number  of  beer  or  ale  gallons  ;  and  di- 
Tide  the  product  by  2730  and  the  q"uotient  will  be  the 
Bumber  of  bushels. 

J\'oie.  The  above  numbers  for  divisors  are  found  by  di- 
viding 231,  282  and  2150,4,  by  the  deeimal  ,7854. 

EXAMPLE.  Required  the  number  of  w?ne  gullons,  in  the 
cylinder  delineated  in  the  figure  of  problem  4,  of  mensur- 
ation. The  diameter  of  its  base,  being  5  feet  =  CO  inches , 
and  the  length  13  feet  =  156  inches. 

60  294,12)  ^^61600,00  (1909,42  Ans. 

60  29412 


3G00  267480 

t56  264708 


21600  277200 
18000  264708 
3600  


124920 


561600  dividend.  117648 


72720 


Here  observe,  that  two  cyphers  are  affixed  to  the  pro- 
dDct  to  equal  the  nomber  of  decimals  in  the  divisor,  which 
makes  the  quotient  the  number  of  gallons  :  but  the  other 
cyphers  added  to  the  remaiQder,  gives  decimals. 


GUAGING.  41 


PROBLEM    III. 

To  find  the  number  of  Gallons  or  Bushels  contained  in  a 
body  of  the  form,  of  a  Pyramid  or  Cone.  See  figure  in 
Problem  6,  of  Mensuration. 

Multiply  the  area  of  the  base  of  the  pyramid  or  cone,  by 
one  third  of  its  perpendicular  height  ;  the  product  divided 
by  231  will  give  the  answer  in  wine  gallons;  divide  by 
282  it  will  give  the  answer  in  beer  gallons  ;  and  divide  by 
2>o0,4  and  it  will  give  the  answer  in  bushels. 

EXAMPLE.  Ptequired  the  number  of  beer  gallons,  con- 
tcined  in  a  pyramid,  whose  base  is  30  inches  square,  and 
perpendicular  height  is  60  inches  ? 

30  inches,  side  of  the 
30        square  base. 

900 
20  \  the  height 

Inches  in  a  beer  gal.  282)  18000  (63,8  Ans. 

1692 


1080 


2340 
2256 

84  • 

PROBLEM  IV. 

To  find  the  number  of  Gallons   or  Bushels   contained  in  a 
Vessel  in  the  form  of  a  Frustum  of  a  Cone. 

Multiply  t-he  top  and  bottom  diameters  together,  and  to 
the  product  add  one  third  of  the  square  of  the  dilTerence 
of  the  same  diameters,  then  multiply  this  sum  by  the  per- 
pendicular height,  and  divide  the  product  by  292,12  for 
wine  gallons  ;  by  339,05  for  beer  gallons  ;  and  by  2738 
for  bushels, 

D2 


42 


GUAGIXG. 


EXAMPLE.  Given  the  diaraeter  DC  =40  inclies  ;  the  di- 
ameter AB  =  30  inche?,  and  the  perpendicular  height  FE 
=  60  ioches  5  the  conteats  ia  wine  gallons  are  required. 

F 
40  bottcm  diameter 
30  tap  diameter 

10  dicference 
10 

3)  100  sqr.  of  the  difference     C  (<::T7.'.T:T:::^'i> 


33,3  =i  the  square 

30  (op  diameter 
,40  bottom  diameter 


1200 
33,3 

1233,3 

60  perpendicular  height 


294,12)  73998,00  (231,59  gallcJns,  wine  measiire, 

58824 


151740 
147060 

46800 
29412 

173880 
147060 


268200 


GUAGLXC^. 


43 


PROBLEM   V. 


To  Guage  a  Cask. 

To  guage  a  cask,  measure  the  head  diameters  FA 
and  DC,  and  if  they  differ,  take  the  mean  of  them,  that  is, 
add  the  diameters  of  each  head  together  and  divide  the 
sum  by  2  ;  measure  also  the  diameter  EB  at  the  bung,  ta- 
king the  measure,  inside  of  the  cask  ;  then  measure  the 
length  of  the  cask,  making  due  allowance  for  the  thickness 
of  the  heads  :  Having  these  measures,  you  can  calculate 
the  contents  in  gallons  or  bushels,  by  the  following  rule  : 

Take  the  difference  between  the  head  and  bung  diame- 
ters, maltiply  this  difference  by  ,62  and  add  the  product 
to  the  head  diameter,  the  s.Qm  v^ill  be  (he  mean  diameter  ; 
multiply  the  square  of  this  by  the  length  of  the  cask,  and 
divide  the  product  by  294,12  for  wine,  by  359,03  for  beer 
gallons,  and  by  2733  for  bushels.  The  decimal  ,62  is 
commofily  used  by  guagers,  to  find  the  mean  diameter  > 
but  if  the  staves  are  nearly  straight,  it  would  be  more  accu- 
rate to  use  ,55  or  less.  If  on  the  contrary,  they  are  very 
curving  we  should  use  ,64,  ,65,  or  more.  When  the 
staves  are  straight,  the  decimal  ,61  may  be  used. 

EXAMPLE.  Given  the  bung 
diameter  BE  34,5  inches, 
the  head  diameter  AT  or 
CD=30,7,  after  allowing 
for  the  thicknes  of  the 
heads ;  59,3  inches  the 
length,  find  the  number  of 
wine  gallons  this  cask  will 
Isold, 


44  QUAGINQ. 


34,5  bung  diameter. 
30,7  head      do. 

3,8 
,62 

76 
228 

2,336 
30,7  head  diameter. 


33,056  mean  do. 
33,056 


198336 
165280 
99168 
99168 

1092,699136  call  the  decim.  67 
1092,67 

69,3  length  on  the  in- 

side. 

327801 
983403 
646335 


294,12)  64795,331  (220,3  Ans. 
58824 


59713 
58824 


88931 
88236 


695 

Calipers  are  used  by  gunger?,  in  taking  the  dimensions  of 
casks,  but  a  comuion  rule,  or  a  staif  may  be  usetl.     A  more 


expeditious  way  of  nnchng  the- contents  of  tasks,  is  by  the 
line  of  numbers  on  Gunter's  scale  ;  or  on  the  sliding  rule  ; 
in  order  to  perform  which,  make  marks  on  the  scale,  on 
the  calipers,  at  the  points  17.13  and  18,95  inches  and  at 
o2,33  inches,  which  numbers  are  the  square  roots  of  294,- 
12,  and  359,05,  and  of  2738  respectively.  A  brass  pin  is 
generally  tixed  on  the  calipers  at  each  of  these  points, 
which  are  called  the  guage  points.  Having  prepared  the 
scales  in  this  manner,  you  may  calculate  the  number  of 
gallons  or  bushels,  by  the  following  rule  : 

Extend  from  I  towards  the  left  hand  to  ,62,  or  less,  if  the 
staves  be  nearly  straight  ;  that  extent  will  reach  from* the 
difference  between  the  head  and  bung  diameters,  to  a  num- 
ber at  the  \eti  hand,  which  number  added  to  the  head  di- 
ameter, will  give  the  mean  diameter  ;  then  put  one  fcot  of 
the  compasses  on  the  guage  point  =  17, 15,  for  wine  gallons, 
18,95,  for  beer  gallons,  and  at  52,33,  for  bushels  ;  and  ex- 
tend the  other  fDOt  of  the  compasses  to  a  number  deooting 
the  mean  fiiameter  ;  this  extent  turned  over  twice  the 
same  way  from  the  length  of  the  cask,  will  give  the  num- 
ber of  gallons  or  bushels  respectively. 

In  the  preceding  example,  the  extent  from  1  to  ,62  will 
reach  from  3,8  to  2,4,  nearly,  which  added  to  30,7  gives 
the  mean  diameter  =33,1,  then  the  extent  from  the  guage 
point,  17,15  to  33,1  turned  over  twice  from  the  length  59,- 
3,  will  reach  to  220,9,  wine  gallons.  If  you  had  used  the 
guage  point  18,95  the  answer  would  have  been  in  beer  gal- 
lons ;  or  if  you  had  used  52,33  the  answer  would  have 
been  in  bushels. 

GUAGING  CASKS  BY  THE  SLIDING 

RULE. 

On  the  line  marked  D,  you  may  find  the  guage  point, 
marked  WG  ;  you  will  see  that  you  can  find  17,15  inches, 
a  little  to  the  right  of  the  long  mark,  that  is  over  the  cen- 
tre of  G  ;  also  over  AG  on  the  same  scale  you  will  find  18,- 
95,  or  18|-|,very  near  the  long  mark  over  the  centre  of 
G.'here  is  the  guage  point  for  the  ale  or  beer  gallons,  as 
the  other  was  for  wine  gallons.  Set  the  length  of  the  cask 
found  on  the  slider,  against  the  guage, point  on  D  ;  and  a- 


46  GUAGI.^Z^. 

gainst  the  mean  diameter  on  D,  the  answer  will  be  found 
on  the  slider. 

In  measuring  the  length  of  a  cask,  we  allow  for  the 
thickness  of  both  heads,  1  inch,  l-i  or  2  inches,  according 
to  thei^ize  of  the  cask. 

AoJ'c.  You  must  take  the  hfcad  diameter,  close  to  its 
outside,  and  for  small  casks  add  -^  inch,  for  casks  of  30, 
40,  or  50  gallons,  add  -^  inch,  and  for  larger  casks  add  5 
or  6  tenths  and  the  sum  will  be  very  near  the  head  diame- 
ter within. 

in  taking  the  bung  diameter,  observe  in  moring  the  rod 
or  staff  backward  and  forward,  to  see  if  the  staves  oppo- 
site the  bung,  be  thicker  or  thinner  than  the  rest,  if  so, 
make  the  necessary  allowance. 

EXA3IPLE.  Given  the  bung  diameter  BE=  34,5  inches, 
the  head  diameter  AF,or  CD=30^7  inches. 

34,5. 
Lengthof  the  cask  with-  30,7 

in=59,3.  

£)  65,2 

32,6 
,5 


33,1= mean  diameters 

Now  draw  out  the  shder,  till  59,3  on  the  slider,  coin- 
eides  with  the  L'uage  point  on  the  girt  line,  for  wine  gal- 
lons, and  against  33,1  on  the  girt  line,  will  be  found  on  the 
slider  =220,9  wine  gallons. 

PROBLEM  VI. 

The  gnage  point  for  bushels  is  placed  on  the  girt  line,  at  13,r 
^:^  inches,  as  it  would  run  of  the  rule  on  the  right. — 
For  the  points  for  gallons  i  reverse  it  back  to  the  left  of  those 
points. 

Draw  out  the  slider,  till  the  length  of  a  square  box  or 
bin,  coincides  with  the  guage  point  on  the  girt  line,  to  wit 
against  IS-j^  inches,  then  against  the  number  of  iuche-^ 


OUAGIXG. 


47 


the  box  IS  square,  found  on  the  girt  line  ;  and  on  the  sli- 
der will  be  tbund  the  number  of  bushels. 


EXAMPLES. 

1.  Given  7,75  inches  square  and  30  feet  in  length,   also 
beginning  at  7,75,  and  extend  to  40  inches  square. 

Against  7,75,  will  be  found  10  bushels. 

"  nearly. 


9 

<• 

134  - 

10 

«( 

16|  - 

12 

t« 

24   ♦• 

13,40 

<  < 

30   *^ 

15 

*i 

37|  - 

17 

i< 

48|  ♦' 

19 

*{ 

60   *' 

20 

<4 

661  «' 

21 

M 

73|  - 

24,5 

(( 

100  «* 

25 

«^( 

1045.  '* 

27 

4( 

121^  '* 

29 

(i 

140i  " 

30 

(( 

150  '* 

35 

(( 

208  '* 

40 

(i 

2674-  '' 

**  nearly. 


When  the  bin  is  more  than  40  inches,  say  60  inches,  and 
20  feet  long,  draw  the  slider  to  the  left  hand  till  20  feet, 
the  length  found  on  the  slider,  coincides  with  the  guage 
point  found  on  the  girt  line,  to  wit,  13,385  inches  ;  then 
against  the  width  of  the  bin,  namely  60  inches,  which  found 
on  the  girt  line,  will  be  found  on  the  slider  399,  calling  the 
figures  on  the  girt  line  tens,  and  those  on  the  slider  will 
be  hundreds  ;  and  so  of  any  other  number. 

2.  Suppose  a  bin  30  feet  long,  and  from  40  to  245  inch- 
eB  square. 

Against  40  will  be  found  267  bushels. 


60  ' 

5981 

100  ' 

1675 

120  * 

[            (C 

2500 

150  ' 

3790 

190  * 

6000 

245  ^' 

9950 

43  CASTl.yQ  LXTEREST  O.V  THE  >LfDiyQ  RULE. 

To  find  how  many  burljels  any  cylindrical  cask  will  con- 
tain :  or  how  many  bushels  of  timber  any  log  will  contain, 
providing  it  be  a  complete  cylinder. 

Draw  the  slider,  till  the  guage  point,  15,001.  or  nearer, 
lc),0015,  found  on  the  girt  line,  coincides  with  the  length 
of  the  cylinder  in  feet,  found  on  the  sli»3r  ;  then  ag?»iaat 
the  diameter  of  the  cylinder,  found  on  the  girt  line  in  inch- 
es, will  be  the  number  of  bushels  found  on  the  slider. 

EXAMPLE.  Suppose  the  cylinder  300  feet  laid  to  the 
guage  point,  then  against  7,  or  70  inches  for  a  diameter, 
you  will  find  6444  bushels,  the  answer  on  the  slider. 

TO    CUT    OFF    ANY    ?  ?  MBER    OF    CUBIC    FEET    OF 
ANT    DIAMETER,    OF    ROUND    TIMBER. 

Suppose  the  number  of  feet  required  to  be  cut  off,  be  3, 
and  the  diameter  be  T-i-  mches. 

Draw  out  the  slider  till  3  coincides  with  7i  on  the  fixed 
part,  then  against  the  guage  point  13,54  inches  will  be 
found  the  length  to  be  cut  off. 

EXAMPLES, 

1.  If  ^2jl5buy  1  foot  of  timber  how  much  will  jllO 
buy  ?  4, G5  cubic  feet,  Ans. 

2.  This  timber  is  4,3  inches  in  diameter  ;  what  is  the 
length  of  the  stick  ? 

Lay  4,65  feet  on  the  slider,  against  4,3  inches,  on  the 
girt  line,  and  against  13,54  inches  on  the  girt  line  will  be 
found  46,5  feet,  the  length  of  the  stick  on  the  slider. 

For  square  timber,  draw  the  slider  so  that  the  number 
of  inches  the  stick  is  square,  found  on  the  fixed  part,  co- 
incides with  the  number  of  feet  on  the  siller  :  then  against 
12  will  be  fou43d  the  number  of  feet  in  length  to  be  cut  off 

TO    CAST  INTEREST  ON  THE  SLIDING  RULE  FOR 

ONE  YEAR. 

Let  the  priocipd  or  numbar  of  dollars  be  found  on  A, 
and  put  the  per  cent  on  the  slif'er  agaii.?t  the  centre  1  ; 
then  against  the  principal,  will  be  found  the  interest,  calling 
dollars,  cents.     To  cast  interest  for  days,  firtd  th*  days  for 


GASTIXG  LXTEREST  OX  THE  SLIDIXG  RULE.  49 

one  year  or  3G5,  on  the  fixed  part  A  ;  then  draw  the  sli- 
der till  the  interest  for  one  year  betore  found,  coincide 
with  the  365  days  ;  now,  on  the  fiied  part  A,  noiice  the 
number  of  days  you  want  to  get  the  interest  for,  and  under 
that  on  the  slider,  will  be  found  the  interest;  for  tlie  davs 
required. 

EXAMPLES. 

1  What  is  the  interest  g333,33  for  one  year  and  twenty = 
five  days,  at  6  per  cent.  First  for  one  year,  by  the  above 
directions,  will  be  lound  <^20  ;  now  notice  365  days  on  A, 
and  draw  the  slider  till  g20  coincides  with  it  or  under  365 
days,  then  look  for  25  days  on  A,  and  on  B,  under  25  will 
be  ct  1.33- the  answer  for  25  days. 

2  What  is  the  interest  of  j^^lOOO  for  one  year  and  thirty 
SIX  days  at  7  per  cent.  Draw  out  the  slider  till  7  on  the 
slider  coincides  with  the  centre  1  and  against  1000  on  the 
right  hand  at  A,  will  be  found  70  on  the  slider.  Then  lay 
70  on  the  slider  against  365  days  on  the  tised  part  and 
against  3d  on  the  slider  will  be  found  g6,oo     Ans.  ;^76,88. 


A  Tahle^  for  the  use  of  Coopers^  in  calculaiing  Cisterns, 


Wine  gallocs 
and  parts  of 
sralions. 


•i^O  ®Q  >-  GN  O  G^  o 


s^ 


i^  o  '-"  e<  cj  T-.  o 


^  O  Lj  u'i  o  O  1>  O  ^':  ^n  !>  CO  !??  i^i  »-»  CO  L-)  ft) 

o  c:  'o  G)  —  .ri  j>  SD  t-  CO  cc  T  —'  c^  G)  T*'  -1-  '?4 
i-Oxocot-cococriO^'?^rii--:;t>coco~co(:o 


Smallest  head  i?  x'  ;r  "-^  ^  O  o  g<  -r  •:c  o:  c  C  o^  O  ~  ^  t- 
i«    feet    and    ^  --  --'  ^  ^  "  O  O  o  o  o  -  o  C  O  6  O  C 


mche?. 


Largest  head 
in  feet  aad 
incl.es. 


"^  "^  "^  -f  "j^  -♦•  ^"^ 


t-O  u*;  lit-  xQ  lq  o  tc  cr  uo  ^o  o 


T»  up  lr^  ■-?  u^  o  i^^  tc  to  to  ^.g  i>  r^  t-  {>  t-. 


Depth  of  the  !  2  i^  Z  ":5  ~   '^  ^  '^'  -r  :C'  x  o  O  <rj  -j::  -   c  -o 
cistern  in  feet  i     '  "^  '-'•  '^  ^  '"  ^  '^  '^  ^  -^  ^  O  O  3  O  O  O 


and  inche; 


up  iO  o  iQ  uo  o  -^  '^  o  ^o  to  -o  l>  t-  t-  »-  o:>  CO 


E 


iO 


A  LOG  TABLE. 


A    LOG    TABLE, 

SliOTx-in:^  the  nuiuhcr  cf  feet  of  boards,  {lAt^  lo^  Xi^ill  tnu'i'^i 
whose  diameter^  is  from  lo  to  3Q  inches  at  the  smallest  endy 
Kind  from  10  io  15  feet  ia  length. 


>— 1 

5' 
3 

o 

HI 
1— » 

■rt) 

CD 

CO 

c 

C9 

3 

7^ 

a 

si' 

3 

2. 

wl 

1  ! 

1 

o 

i  ^■ 

3 

o 

5' 

'a 
ti 

5' 

a 

5' 

3 

2 

5" 

3* 
O 

it" 

5' 

1-^ 

5' 

3* 
O 

O 

5' 

a 

15 

yo 

15 

99 

15 

108 

Tr 

117  i 

'td 

126 

15 

135 

16 

100 

16 

MO 

16 

120 

16 

130  1 

16 

140 

16 

150 

17 

125 

17 

137 

17 

150 

17 

160 

17 

175  ! 

17 

187 

'  18 

1 55 

18 

170 

3  8 

186  i 

18 

201 

18 

216 

18 

232 

19 

165 

19 

176 

19 

198  ! 

19 

214 

19 

230 

19 

247 

JO 

172 

20 

189 

20 

206 

20 

263 

20 

246 

20 

258 

21 

184 

21 

202 

21 

220 

21 

238 

21 

256 

21 

276 

',  '22 

194 

22 

212 

1  o<^ 

232 

22 

263 

22 

294 

22 

291 

i2:3 

219 

23 

240 

1  23 

278 

23 

315 

23 

332 

23 

333 

s?^i 

250 

24 

276 

24 

300  ! 

24 

325 

24 

350 

24 

375 

25 

200 

25 

308 

25 

336 

25 

364 

25 

392 

25 

420 

l26 

299 

26 

323 

26 

346 

26 

375 

26 

404 

26 

448 

127 

327 

27 

367 

27 

392 

27 

425 

27 

457  1 

27 

490 

28 

3G0 

28 

396 

28 

432 

28 

462 

28 

504  1 

28 

540 

29 

376 

29 

414 

29 

451 

29 

488 

29 

526 

29 

564 

!30 

412 

3U 

452 

30 

494 

30 

535 

30 

576 

30 

618 

(:>] 

428 

31 

4;i 

31 

513 

31 

558 

31 

602 

31 

642 

;^- 

451 

32 

496 

3'2 

541 

32 

587 

32 

631 

32 

676 

3.: 

490 

33 

539 

33 

588 

33 

637 

33 

686 

33 

735 

^34 

532  1 

|34 

585 

34 

638 

34 

691 

34 

744 

34 

798 

1^5 

582 

35 

640 

ob 

698 

35 

752 

35 

805 

35 

863 

il^. 

593 

iH 

657 

^Q> 

717 

36 

821 

36 

836 

36 

889, 

A  T.1BLE,<^'C. 


61 


.'2  Table  of  Specific  Gravities  of  Bodies. 


Platina  (pure)     -    - 
Fine  Gold      _     -     - 
Standard  Gold     -     - 
Quicksilver  (pure    - 
Quicksilver  (common) 
Lead      _     _     _    _ 
Fine  Silver        -    - 
Standard  Silver       - 
Copper        _     _     - 
Copper  halfpence  - 
Gun  iMetal        -     - 
Cast  Brass         -     - 
Steel     -     -     -     - 
Iron      _     -     _     _ 
Cast  Iron    -     -     - 
Tin       -     -     -     - 
Clear  Crystal  Glass 
Granite       _     -     - 
Marble  and  hard  stone 
Common  green  Glass 
Flint       -    -    -    - 
Common  Stone        - 


SSOOO'Clay 
19400  Brick 


17724 

14000 

1 3600 

1132o 

11091 

10535 

9000 

8915 

8784 

8000 


Common  Earth  -  - 

Nitre        _     _     -  _. 

Ivory        _-     _     -  _ 

Brimstone      ~     -  _ 

Solid  Gunpowder  - 

Sand   -     _     -     -  - 

Coal   -     -     -     -  - 

Box-wood       _     -  — 

Sea-water       —     -  - 

Common-water    -  - 


7850  Oak     -     - 


7645 

7425 

7320^Ash 

3150 

3000 

2700 

2600 

2570 

2520 


Gunpowder,  close  shake 
Ditto,  in  a  loose  heap 


iMapIe  -  -  -  - 
Elm  _  -.  _  . 
Fir  _  -  _  - 
Charcoal  -  -  - 
Cork  _  -  -  - 
Air  at  a  mean  state 


2160- 

2000 

1984 

1900 

1826 

1810 

1745 

1520 

1250 

1030 

1030 

1000 

925 

n93T 

83G 

836 

too 

600 

550 

240 


Kote,  The  several  sorts  of  wood  are  sujjposed  to  be  dr3\ 
Also,  as  a  cubic  foot  of  water  weighs  just  1000  ounces  a- 
voirdupois,  the  numbers  in  this'table  express,  not  only  the 
specific  gravities  of  the  several  bodies,  but  also  the  weight 
of  a  cubic  foot  of  each,  in  avoirdupois  ounces  ;  and  there- 
fore, by  proportion,  the  weight  of  any  other  quantity,  or 
the  quantity  of  any  other  weight,  may  be  known,  as  in  Ihe^ 
next  two  propositions. 


PROPOSITION    I. 


To  find  the  Mapiitude  of  any  Body,  from  its  Jf'ei^ht, 

As  the  tabular  specific  gravity  of  the  body, 
Is  to  its  weisfht  in  avoirdupois  ounces, 
So  is  one  cubic  foot,  or  1728  cubic  inches, 
To  its  contents  in  teet,  or  inches,  respectively. 


TO  FIND  THE  WEIGHT  OF  A  BODY,  4'c. 

EXAMPLES. 

1.  Required  the  contents  of  an  irregular  block  ofcom- 
:   stone,  which  weighs  1  cwt.  or  112  lb  ? 

Ans.   1228|f  l-l  cubic  irxhes. 

2.  How  many  cubic  inches  of  gunpowder  are  there   in 
lb.  weight  ?  Ans.  29|-  cubic  inches  nearly. 

3.  How  many  cubic  feet  are  there  in  a  ton  weiglit  of 
ry  oak  ?  Ans.  38i|f  cubic  feet. 

FHOrOSITION  II. 

To  fiyid  ike  Weight  of  a  Body  from  its  Magnitude. 

As  one  cubic  foot,  or  1728  cubic  inches, 
Ih  to  the  contents  of  the  body, 
So  is  the  tabular  sy)ecific  gravity, 
To  the  weight  of  the  body. 

EXAMPLES. 

1.  Required  the  weight  of  a  block  of  marble,  whose 
englh  is  63  (eet,  and  breadth  and  thickness  each  12  feet  ; 
eing  the  .dimensions  of  one  of  the  stones  in  the  walls  of 
"albeck  ? 

Ans.  603,-^  ton,  which  is  nearly  equal  to  the  burden  of 
A)  East- India  ship. 

2.  What  is  the  weight  of  1  pint  ale  measure,  of  gunpow- 
der ?  Ans.  19  oz.  nearly. 

3.  What  is  the  weight  qf  a  block  of  dry  oak,  which 
measures  10  feet  in  length,  3  feet  broad,  li  feet  deep  or 
thick  ?  Ans.  4335f|  lb. 


A  TABLE  OF  SOLID  MEASURE 
OF  SQUAPtE  TIMBER, 

By  the  following  Table  the  solid  contents,  and  the  value 
of  any  piece  or  quantity  of  timber  stone  &c.  may  be  found 
at  si^ht,  from  6  inches  to  29-^  inches,  the  side  of  the  square, 
or  one  fourth  of  the  girt  ;  and  from  14  feet  to  92  feet  in 
lengih.  It  rises  from  6  inches,  -  inch  at  a  time  till  it  rises, 
to  29*  inche?,  and  from  14  feet,  1  foot  at  a  time  till  it  rises 


.^  TABLE  OF  SQUARE  TIMBER.  53 

to  92  feet.  The  number  of  inches  which  the  side  of  each 
'Stick  measures  are  placed  at  the  top  of  the  two  first  or 
lei't  hand  columns,  and  at  the  top  of  the  two  columns  at 
the  right  hand  of  each  double  line.  These  columns  £;ive 
the  length  and  contents  of  each  stick,  and  the  other  two 
columns  which  run  from  the  top  to  the  bottom  of  the  pa^e 
are  a  continuation  of  the  two  first;  so  the  len^j-th  of  the 
stick  will  be  found  in  the  first  and  third  column  from  the 
left  hand  of  the  page,  and  from  the  right  hand  of  each 
double  line  ;  and  in  the  second  and  fourth  columns  the 
contents.  The  half  feet  are  not  reckoned  ;  that  is,  when  a 
stick  measures,  for  exanple,  30  cubic  feet  and  5  inches 
it  is  reckoned  only  30  feet,  and  if  it  measures  30  cubic 
feet  and  7  inches  it  is  reckoned  31  feet,  &c.  this  is  the 
method  of  reckoning  timber  in  Quebec  and  Montreal,  ard 
"In  all  markets  in  the  United  States. 


A  TABLE  OF  Sqi\3RE  TIMBER 


side  d  1 

61 

IS.'SiJe  6> 

51 

1  o-i-"^5ae  7 

51 

17.j=ic 

e  Tt  5\  20: 

•x 

las. 

52 

13 

.- 

Ids. 

52 

15! 

"■-* 

1  Ins. 

52 

17: 

\ — 

I"^-;  52  20: 

0 

c 

00 

54 

56 

13 
13 

^-1 

if 
is 

0 

53 
54 

?? 
06 

161 
16' 
16; 

2 

j 

53 
54 
55 

06 

IS 
181 
18' 

19! 

^ 

53 
!54 
bb 
56 

2C- 

21 

21 

22 

il4 

3 

14 

114! 

4 

i6i 

14 

5 

M 

5 

115 

4 

14!15| 

4 

57 

17;jl5 

5 

57 

i9;;i5 

.     6 '157 

22 

\V3 

4;58 

M 

:16 

5 

58 

17!lie 

5 

58 

19;|16 

6;!58 

22 

!l7 

415? 

1  Oil  17 

5 

59 

17:|r7 

6 

59 

'  20;ll7 

6\ 

59 

^ 

:-60 

15;jl8 

5 

60 

18'!l8 

6 

60 

20;ll£ 

7I 

60 

23 

l-^i 

15*10 

G 

61 

IS'  19 

6 

61 

20|*19 

7. 

61 

24 

.  1  -,  ^ 

•jo- 

15120 

6 

62 

18;  20 

7 

62 

21;  20 

si 

62 

24 

-i 

0  IJC 

1621 

6 

6S 

18;j2i 

7 

00 

21;  21 

S| 

63 

24 

*i£' 

5  C4 

16!i22 

6 

64 

7 

64 

21  22 

•  1 

81 

64 

25 

23 

6 

60 

16|23 
16it24 

7 

63 

IS- 

23 

0 

65 

00'   O-D 

9i 

65 

25; 

;24 

6 

66 

7 

66 

19 

24| 

8 

ge 

22  1^4 

A" 

9:|66 

26! 

^25 

6 

67 

17|i25 

"7 

67 

20! 

2c 

8 

67 

22!!25 

10167 

26 

l>6 

6 

68 

I7|2e 

8 

68 

20! 

2c 

9 

68 

23l|26 

10' 68 

26 

1:27 

r- 
/ 

6P 

17*27 

8 

69 

20' 

27 

9 

69 

23  27 

10l69 

271 

■on 

7 

70 

171  28 

8 

70 

21: 

00 

9 

70 

23;  28 

11  70 
lli71 

27, 

129 

7J 

18=29 

9 

71 
72 

2lj|29 

10 

71 

24|  29 

27 

;:^o 

72 

jSjISO 

9 

21;  30 

10 

72 

24:30 

11|72 

28 

ol 

c 

73 

18' 31 

973 

2lj 

31 

10 

73 

25131 

12173 

281 

32 

74 

18;  32 

19133 

977 

22; 

32 

11 

74 

25^32 

12  74 

13  75 

29! 

"33 

8 

75 

10;75 

22i 

33 

11 

75 

25i  .33 

23| 

34 

r 

76 

19134 

10i76 

22  34 

11 

1^  n- 
.'O 

26;  34 

13  76 

29i 

'^5 

9 

77 

19j  35 
191  3e 

10j77 

23^35 

12 

77 

26  35 

13  77 

30i 

3G 

p 

It 

11{78 

23]36 

12 

78 

26)36 

14i78 

30 

-?? 

c 

69 

20;;37 

il|79 

23;  37 

12 

79 

27:  37 

14179 

31 

c 

2V 

20;|30 

III8O 

23  38 

13 

80 

27  38 

15j 

80 

31 

■  '9 

!0 

81 

£0;!39 

ii;3i 

24  ;39 

13 

81 

27139 

l^i 

81  31 

'40 

10 

32 
83 

20;i40 

12:82 

24.  40 

13 

82 

28'j40 

Vo^. 

8232 

Ui 

10 

2^1 

41 

12  83 

24:41 

14 

83 

28  41 

161 

8332 

:ie 

w 

84 

21; 

42 

12J84 

25  42 

14 

84 

28.42 

16itC4J33 

i43 

11 

85 

21 

13 

13  85 

25|J43 

14 

85 

29,  43 

17ii85  331 

■44 

11 

86 

,21; 

44 

13  86 

2544 
25145 

15 

86 

29:  44 

17186 

34 

!45 

11 

37 

22' 

45 

13'S7 

15 

87 

39::45 

17  87 

3« 

16 

11 

88 

-ogl 

46 

1380 

26;i46 

15 

88 

30^  46 

18 '88 

34! 

■47 

12 

79 

22';  17 

14;89 

2l-.i47 

16 

89 

30I47 

18 

80 

351 

;tp 

IC 

9t'> 

22,148 

Hiso 

2o! 

48 

16 

9C 

30' 

48 

19 

90 

35 

:  ' 

K- 

91 

23f  49 

14;9i 

-"i 

49 

16 

91 

31! 

49 

19 

91 

35| 

l?i99 

23156 

lo92 

271 

50 

17 

92 

31 '=50 

19jl92!36' 

A  TABLE  OF  SQUARE  TIMBER. 


55 


Side  8 

51 

22 

Side  8i 

i'5l 

1  C)c 

Side  9 

51 

281  Side  9| 

51 

32 

hr- 

lus. 

5'Z 

23 

^ 

Ins 

1 

52 

1  26 

►t- 

Ins 

52 

29  1  - 

Ins. 

52 

32 

<rt- 

o' 

O 
o 

55 
5£ 

.  23 
24 

24 

'o 

>-< 

O 

c 

^3 
54 
55 

26 

27 
27 

(-r 

o" 

Ot9 

O 

o 

in 

53 
54 

55 

30 
31 
31 

o' 

g 

53 

54 
55 

33 

34 
34 

14 

"~6 

56 

25 

14 

7 

56 

28 

14 

s 

56 

32 

14 

9 

66 

36 

15 

6 

57 

25 

15 

7 

57 

28 

15 

8 

57 

32 

15 

9 

57 

36 

16 

7 

58 

26 

16 

8 

58 

29 

16 

9 

58 

33 

16 

10 

58 

36 

17 

7 

59 

26 

17 

8 

59 

29 

17 

9 

59 

33 

17 

10 

59 

37 

18 

8 

60 

26 

18 

9 

60 

30 

18 

10 

60 

34 

18 

11 

60 

37 

19 

8 

<n 

27 

19 

9 

61 

30 

19 

10 

61 

34 

19 

12 

61 

38 

20 

9 

62 

27 

20 

10 

62 

31 

20 

11 

62 

35 

20 

12 

62 

39 

21 

9 

63 

28 

21 

10 

63 

31 

21 

12 

63 

35 

21 

13 

63 

39 

22 

10 

64 

28 

22 

11 

64 

32 

22 

12 

64 

36 

22 

14 

64 

40 

23 

10 

65 

.29 

23 

11 

65 

32 

23 

13 

65 

36 

23 

14 

65 

41 

24 

10 

66 

29 

24 

12 

66 

33 

24 

13 

66 

37 

24 

15166 

41 

25 

11 

67 

30 

25 

12 

66 

33 

25 

14 

61 

37 

25 

15167 

42 

26 

11 

68 

30 

26 

13 

68 

34 

26 

14 

68 

38 

26 

16  68 

42 

27 

12 

69 

30 

27 

13 

69 

34 

27 

15169 

39 

2'^ 

1769 

43 

28 

12 

70 

31 

28 

14 

70 

35 

28 

16 

70 

39 

128 

18j70 

44 

29 

131 

71 

31 

29 

14 

71 

35 

29 

16 

71 

40 

129 

18  71 

44 

30 

13i 

72 

32 

30 

15 

72 

36 

30 

17 

72 

40 

I'SO 

19j72 

45 

31 

14 

73 

32 

21 

15 

73 

36 

31 

17  73 

41 

|31 

19  73 

40 

32 

14 

74 

33 

32 

16 

74 

37 

32 

18 

74 

41 

'32 

20  74 

46 

33 

14! 

75 

33 

33 

16 

76 

O  1 

33 

18 

75 

42 

;33 

20  75 

47 

34 

15! 

76 

34 

34 

17 

76 

38 

34 

19 

76 

43;34 

2176 

47 

35 

15! 

77 

34 

35 

17 

77 

38 

^^5 

19 

77 

44 

35 

22  77 

48 

36 

16i 

78 

34 

36 

18  78i 

39  36 

20 

78 

44 

36 

23  78 

49 

37 

16' 

79 

35 

37 

18 

79 

39  37 

21 

79 

45 

37 

23  79 

49 

38 

17; 

80 

35 

38 

19 

80 

401  38 

21 

80 

45 

1  o  c 

24!8C 

50 

39 

17; 

81 

36 

39 

19 

8] 

4ll39 

22 

81 

45 

39 

24'81 

51 

40 

18| 

82 

36 

40 

20 

82 

41' 40 

22 

8f 

A6 

40 

25|82 

51 

41 

is! 

83 

37i 

41 

21 

83 

42'' 

4l 

23 

83 

47 

41 

25|8S 

62 

42 

18i 

84 

37[ 

42 

21 

84 

42 

4o 

23 

84 

47 

42 

26184 

52 

43 

19 

85 

38 

43 

21 

85 

43 

43 

24 

85 

48 

43 

27!85 

63 

44 

19 

86 

38 

44 

22 

86 

43 

44 

25 

86 

48 

44 

27(80 

54 

46 

20; 

87 

38 

45 

22 

37 

44 

45 

25 

87 

59 

45 

28  87 

54 

46 

20 

88 

39 

46 

23 

38 

44 

46 

26 

88 

49 

46 

29  88 

56 

i7 

21 

39 

39 

47 

23 

30 

44 

47 

26 

R9 

50 

47 

29  89 

65 

48 

21 

90 

40 

48 

24 

?0 

46 

48 

27 

30 

51  i 

48 

3090 

56| 

49 

22 

91 

40 

49 

24. 

n 

46  • 

49 

£7 

91 

51 ; 

49 

30  91 

57 

50 

22 

52 

41 

50 

2^< 

D2 

46 

50 

28j03| 

52  i 

50 

31;92 

581 

1 

A  TABLE  OF  SqUARE  TIMBER. 


fSide  10 

51 

35 

Sidel0^)51 

39: 

Side  1 1 

51 

43 

Side  11^ 

51 

47 

i"^ 

Ins. 

52 

36 

n- 

la?. 

52 

40! 

'^ 

Ins. 

52 

43 

T- 

Ids. 

52 

48 

D 
j  1' 

O 

o 

3 
<-•■ 
en 

9 

53 
54 

55 

56 

37 

37 
38 
39 

O 

o 

• 

53 

54 
55 
56 

4l| 
42| 
42i 
43' 

0 
b 

~I2 

53 
54 
55 

50 

44 
45 
46 
47 

3 

0 
0 

3 

63 
54 

55 
56 

4fl 
5C 
51 

u 

10 

T4 

13 

52 

;i5 

10 

57 

39 

15 

11 

O  i 

44 

15 

12 

57 

48 

15 

14 

57 

62 

:i6 

11 

58 

40 

16 

12 

58 

44|ilG 

13 

58 

49 

|16 

14 

58 

54 

il7 

12 

59 

41 

17 

13 

59 

45', 

17 

14 

59 

49 

17 

15 

59 

55 

18 

13 

60 

41 

18 

14 

60 

46' 

18 

15 

60 

50 

18 

16 

60 

56 

19 

14 

61 

42 

!l& 

14 

61 

47| 

19 

16 

61 

51 

19 

17 

6\ 

66 

20 

15 

62 

43 

20 

15 

62 

47 

20 

17 

62 

52 

20 

18 

62 

68 

21 

15 

63 

44 

21 

16 

63 

48, 

21 

17 

63 

53 

21 

19 

63 

69 

22 

16 

64 

44 

22 

17 

64 

60 

22 

18 

64 

54 

22 

20 

64 

59 

23 

16 

65 

45 

23 

17 

65 

50 

23 

19 

65 

54 

23 

21 

6b 

60 

24 

17 

66 

46 

24 

18 

66 

5l' 

24 

20 

66 

65i 

24 

22 

66 

61 

25 

17 

67 

46 

25 

19 

61 

52 

25 

21 

67 

56| 

25 

23 

61 

62 

26 

18 

68 

47 

-26 

20 

68 

52j 

26 

22 

68 

67( 

26 

24 

68 

62 

27 

19 

69 

48| 

27 

20 

69 

53| 

27 

22 

69 

58 

27 

25 

69 

63 

28 

20 

70 

48; 

28 

21 

70 

54: 

28 

23 

70 

59 

28 

or: 
^0 

70 

64 

29 

20 

71 

491129 

22 

71 

54 

29 

24 

71 

59 

39 

2C 

71 

65 

!30 

21 

72 

50' 

130 

23 

72 

55 

30 

25 

72 

60 

30 

27 

72 

66 

131 

21 

73 

50 

31 

23 

73 

66' 

31 

26 

73 

61 

31 

28 

73 

61 

32 

22 

74 

51 

32 

24 

74 

57; 

32 

27 

'i 

62 

32 

29 

74 

68 

33 

33 

75 

52| 

33 

25 

75 

67, 

33 

27 

75 

63 

33 

30 

75 

69 

31 

24 

76 

53! 

34 

26 

76 

58! 

34 

28 

66 

641 

34 

31 

76 

70 

35 

24 

77 

53 

35 

27 

77 

59! 

35 

29 

74 

641 

25 

32 

77 

71 

36 

25 

78 

54 

36 

27 

78 

59 

36 

30 

78 

65 

36 

39 

78 

71 

37 

26 

79 

55 

37 

28 

79 

60| 

37 

31 

79 

66\ 

37 

34 

79 

72 

38 

27 

80 

oo 

38 

29 

80 

61| 

38 

32 

80 

67 

38 

35 

80 

39 

27 

81 

56 

39 

30 

81 

621 

'l>d 

33 

81 

68| 

39 

3G 

81 

74 

40 

28 

82 

57 

40 

30 

82 

63 

40 

33 

82 

69 

40 

36 

82 

t  c- 

41 

29 

83 

57 

41 

31 

83 

63 

11 

34 

83 

70 

41 

37 

83 

7C 

!42 

29 

84 

58 

42 

32 

84 

64 

13 

35 

84 

70 

42 

38 

84 

i43 

30 

85 

59 

43 

33 

85 

65 

43 

36 

85 

71 

43 

39 

85 

78 

44 

30 

86 

60 

44 

34 

86 

66 

44 

37 

86 

72 

44 

40 

86 

6r 

45 

31 

87 

60 

25 

35 

87' 

61 

45 

38 

87 

73 

45 

41 

87 

SO 

;40 

32 

88 

61 

46 

35 

88 

67 

46 

38 

88 

74 

46 

42 

88 

C'' 

J47 

33 

89 

C2 

47 

36 

89 

68 

47 

39 

8S 

75 

47 

43 

89 

81 

148 

33  90 

a 

48 

37 

90 

69 

48 

40 

90 

75 

48 

44 

9G 

82 

|49 

34  91 

63 

49 

38 

91 

70 

49 

41 

91 

76 

4r 

45 

01 

iS 

joO 

34l92 

64i 

50 

38  92 

7^ 

50 

42 

9- 

-77 

■;•" 

,.^^g. 

'4 

A  TABLE  OF  SqUARE  TIMBER. 


.Side  12 

51 

51 

3idel2^?5l! 

55| 

Sid 

e  13151 1  60ilSidel3-^ 

51  64' 

1 

Ins. 

52 

52 

-^ 

Ins.|5o 

56 

'hr* 

Ins.! 

52 

61j  - 

lus. 

52 

66 

o' 

3 

1  aq 

O 
o 

D 

53 

54 
55 

56 

53 
54 
55 
56 

QfQ 

H 

_     IT 

a 

53 
54 
55 

57 

59| 
60| 

O 
£3 

O 

o 

r— 

53 
54 

55 
56 

62 
63 
64 

66 

u 

O 
o 

3 

17 

53 

54 
56 
56 

67 
68 
69 
71 

H 

14 

15  56 

H 

~16 

15 

15 

57 

57 

15 

16  57 

62 

15 

17  57 

67 

15 

19 

57 

72 

16 

16 

58 

58 

16 

1758 

63 

16 

19 

58 

68 

)6 

20 

58|  73 

17 

17 

59 

59 

17 

18  59 

64 

17 

20 

59 

69 

17 

21 

59 

74 

18 

18 

60 

60 

18 

19  60 

65 

18 

21 

60 

70 

18 

23 

60 

76 

19 

19 

61 

61 

19 

2161 

66 

19 

22 

61 

71 

19 

24 

61 

77 

20 

20 

62 

62 

20 

22  62 

67 

20 

23 

62 

73 

20 

25 

62 

78 

|21 

21 

63 

63 

21 

23  63 

68 

21 

25 

63 

74 

21 

26 

63 

79 

i22 

22 

04 

64 

22 

24  64 

69 

22 

26 

64 

75 

22 

28 

6-^ 

81 

23 

23 

65 

65 

23 

25  65 

71 

23 

27 

65 

76 

23 

29 

65 

82 

24 

24 

66 

66 

24 

26  66 

72 

24 

58 

66 

77 

24 

30 

6o 

83 

25 

25 

67 

97 

25 

2767 

^73 

25 

29 

'61 

78 

25 

31 

67 

85 

26 

26 

68 

68! 

26 

2868 

74 

26 

30 

'68 

80 

—  c 

33 

68 

86 

27 

27 

69 

69 

27 

2969 

75 

27 

32 

69 

81 

27 

34 

69 

87 

28 

28 

70 

70 

28 

3070 

76 

Vc< 

33 

j70 

82 

2b 

35 

70 

88 

29 

2971 

71 

29 

3171 

77 

29 

34 

71 

83 

?.9 

36 

71 

90 

30 

30  72 

72 

30 

33|72 

no 

30 

35 

72 

84 

30 

38!72 

91 

31 

3173 

73 

31 

34  73 

79 

1 

36 

'73 

85 

31 

39 

73 

62 

32 

32  74 

74 

32 

35  74 

80 

38 

'74 

87 

32 

40 

74 

93 

33 

33  75 

75 

33 

36  75 

81 

33 

39 

to 

88 

33 

42 

76 

95 

34 

34176 

76 

34 

377C 

82 

34 

40 

16 

89 

34 

43 

76  26 

35 

35  77 

77 

35 

38|77 

83 

35 

41 

77 

90 

35 

44 

67  97 

36 

36  78 

78 

36 

39^78 

84 

36 

42 

78 

91 

o- 

45 

78 

98 

37 

37  79 

79 

37 

40379 

86 

37 

43 

79 

92 

37 

47 

79 

I'OO 

38 

38  80 

8C 

33 

4l|80 

87 

38 

44 

80 

94 

38 

48 

80 

101 

39 

3981 

81 

39 

42^81 

88 

39 

46  81 

95 

39 

49 

81 

102 

40 

40  82 

82 

40 

43:82 

89 

40 

4  7  82 

96 

40 

50 

82 

103 

41 

4183 

83 

41 

44J83 

90 

41 

48  83 

97 

41 

62 

83 

105 

42 

42  84 

84 

42 

45  84 

46  85 
48*86 

91 

42 

49  84 

99 

42 

53 

84 

106 

43 

43^85 

85 

43 

92 

43 

50  85 

100 

43 

54 

85 

107 

44 

44^86 

86 

44 

93 

44 

5186 

101 

44 

55 

86 

109 

45 

■45|87 

8- 

M  ^. 

49  87 

94 

45 

53:87 

102 

45 

57 

87 

no 

4^ 

46|88 

-88 

46 

50  88 

95 

46 

54 

88 

103 

46 

58 

88 

111 

47 

47J89 

89 

47 

51|89 

96 

47 

55 

89 

104 

47 

59 

89 

112 

48 

48:30 

■  9C 

48 

52j90 

97 

48 

56 

90 

105 

48 

60 

90 

114 

49 

49191 

91 

49 

53|91 

98 

49 

57 

91 

106 

49 

62 

91 

115 

(50 

5C 

)j92 

92 

50 

54192 

100 

50 

58 

92 

108 

50 

63 

92 

116 

.1  xAIjLL  Oh  ^^iLAllE  TIMBER. 


•Side  14 

l~5 

In?. 

1  ■3\ 

© 

il4 

~T9 

15 

20 

116 

22 

17 

23 

18 

24 

19 

26 

20 

27 

21 

28 

22 

30 

23 

31 

24 

32 

25 

34 

26 

35 

27 

37 

28 

38 

29 

39 

30 

41 

31 

42 

32 

43 

33 

45 

24 

46 

35 

47 

36 

49 

37 

50 

38 

51 

39 

53 

40 

54 

41 

55 

42 

57 

43 

58 

44 

GO 

45 

61 

41 

62 

47 

64 

A? 

65 

49 

66 

h 

68 

? 


51  i 

52 

-  o 

oo 
54 

55 
56 
57 
58 
59 
60 
61 
62 
63 
64 
65 

67 
68 
69 
70 
71 
72 
73 
74 
75 
76 
77 
78 
79 
80 
81 
82 
83 
84 
Z'- 

8'-; 

n  n 
OO 

s-^ 

90 

CI 
92 


691  Sid 
71 


72! 


7  0 

75 
76'[14 


77 

79 


el  4.^ 
Ins. 


80!il7 


81 

83 

84 

86 

87 

88 

90 

91 

92 

94 

95 

96 

98 

99 

100 

102 

103 

104 

106 

107 

108 

no 
111 

113 
114 

n 
ii' 

ir^ 

1? 

K-1 

122 
1  ?.\ 
125 


1 

19- 

120 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
12 
43 
14 


o 


20 
22 
23 
25 
26 
27 
29 
30 
32|64 


33 
35 
36 
38 
39 
41 
42 
44 
45 
46 
48 
49 
51 
52 
54 


51 
52 
oo 
54 
55 
56 
57 
58 
59 
60 
61 
62 
63 


65 
66 
67 
68 
69 
70 
71 
72 
73 
74 
75 
76 
,77 
78 
79 


55'80 


67 
58 
60 
61 
63 
64 
65 
67 
68 
70 
71 
73 


81 
85 
83 
84 
85 

8': 

8": 

88' 

8C 

90 

91 

9'i 


74 

76 

77 

79 

80 

82 

83 

84 

86 

87 

89 

.90 

92 

93 

95 

96 

98 

99 

101 

102 

103 

105 

106 

108 

109 

111 

112 

114 

115 

117 

118 

119 

121 

122 

124 

12C 

127 

128 

i30 

131 

133 

134 


Side  15 
—  Ins. 


c 
05 

15 
16 
17 
18 
19 
20 
21 
22 
|23 
j24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
M 
45 
46 
47 
48 
49 


c 


22 
2o 
25 
26 
28 
29 
31 
33 
34 
36 
37 
39 
40 
42 
44 
45 
47 
48 
50 
51 
53 
54 
56 
58 
59 
61 
62 
64 
65 
67 


51 

52 
00 
54 
55 
56 
57 
58 
59 
60 
31 
32 
63 
64 
65 
6G 
67 
68 
69 
70 
71 
72 
73 
74 
75 
76 
77 
78 
79 
80 
81 
82 
80 
84 
85 


69.8^ 

70|87 

72188 

7389 

7590 

76  91 

7892 


79 

81 

82 

84 

86 

87 

89 

90 

92 

94 

95 

97 

98 

100 

lOi 

103 

105 

106 

108 

109 

111 

112 

114 

115 

117 

119 

120 

122 

123 

125 

126 

128 

129 

131 

133 

134 

136 

138 

139 

140 

142 

144 


46 
47 
48 
49 
50 


23:56 
25157 


26 
28 
30 
31 
33 
00 
36 
38 
40 
41 
43 
45 
46 
48 
50 
51 


P! 


00 


60 

66 


Sidel>.^61 
.  I  Ins.  no 

Ci   n  !53 

14 
15 
16 
17 

18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 


85; 
87t 

90 

92! 
93! 
95i 
97i 
98! 


60!100| 

6IJIO2I 
62  103 


10 


O", 


64(106 


108; 
110 


671112 
68|ll3 
69  115 
70!ll7 
71I1I8 
72!l20f 


73 


53  74 
5575 
66176 
58  77 


60 
61 


78 
79 


J  22 
124 
125 

127 
128! 
130 
132 


63  80  133 


65 


66  82 
68'83 


70 
71 
73 
75 
76 
78 


84 
85 
86 
87 


135 
136 
138 
140j 
142 
143 
145 
147 


89  148 


80  90J150 
8291tl52i 
83J92ll53j 


j«^ 


A  TABLE  OF  6qUARE  TlMBtlR, 


b'J 


<  Ins. 


31  3 


I4i 

!:> 

16 

17 

18 

19 

20 

21 

22 

23| 

24 

25 

26 

27 

28 

29! 

;o| 

31 

12 
3o 
64 

35 
36 
37 

3b 

39 

4i 

41 

42 

43 

44 

45 

4r- 

47 

4b 

4i 

5o 


25 

26 

28 

30 

32 

3^ 

o5 

27 

39 

4i 

42 

44 

46 

48 

5' 

51 

53 

b5 

57 

58 

60 

62 

64 


J  1 

52I 

54. 

551 

jf 

37 

58 

5  -- 

60 

61 

62 

63 

6<:i 

,  I 
05i 

6 

67 

68 

70 

7 
I 

72 
7o 
74 
75 
7t- 
77 


9ui  3  de\6^ 
Ins. 


■7'^ 
80  1 


82 

83 


Bi- 


as . 

_90 


9J 

94* 

96| 

■981 

99' 

I0l| 

;o3| 

1051 
106' 
!08| 
i  iO 
1  12 

;  14 

1  15 
I  17 
119 
i2l 
.22 
124 
126 
128 
.30 
131 

I  t>  n 
I  00 

■  35 

137 

138 

i  40 

142 

t  44 

146 

147 

'4v 

iol 

153 

i  54 

•  5t 

158 

i6C 

■62 
164 


14 

!5 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
!27 
28 
29 
30 
31 
32 
33 
34 
35 
|36 

J38 
i39 
1 40 
'41 

t43 

44 

■45 

.4^ 

U7 
148 

'49 


o 


26 
28 

OO 

'"»  -', 
O.C 

v>4- 

^  r 
oL 

38 
39 
4i 
43 
45 
47 
49 
5i 
53 
55 
56 
5£ 
6( 
62 
64 
66 
68 
7u 


72  ^ 

-,81 
6d 


77 
79 
81 
83 
85 
87 
89 
91 
S2 
5i>\   94^ 


82 
83 
84 
85 
86 
87 
88 
89 
9i 


96 

9f 

Ok 

OL 

04 

06 

08 

09 

i  i 

1  o 
15 
17 
19 

2  1 
23 
1,5 
26 
28 
30 

34 
36 
38 

4C 
42 

4t. 
47 
49 
5! 
53 
55 
57 
5r 
61 
63 
64 
6i 
6h 
7(' 
7-2 

9«'  «  f4 


D  1 

2 
5  3 
54 
55 

5C 
57 
58 

59 

DC' 

51 
j2 
63 
64 
o5 
6t' 
67 
68 
69 
70 
71 
7  2 
73 
7u 
75 
66 
77 
78 
'79 


Side  r 
Ins 


16 
.7 
18 
19 
20 
21 
22 
23 
24 
25 
26 
-7 
28 
.9 
3v 
31 
o2 
33 
34 
35 
36 
37 
'8 
39 

i 

-1-2 
43 
44 

4;' 
J.  7 
to 
-19 
50 


28 
30 
32 
3-i 
36 
38 
40 
42 
4"^ 
46 
48 

5 

^  ^ ' 
52  - 
o 


o  I 
52 

55 
5  4 
5  5 
56 
57 
08 
59 
-"C 
ol 
62 
60 
64 


5  6 
58 
CO 
62 
64 
66 
68 
70 
72 


74L 


76 

78 
8< 

32 
64 
S6 


83 

90 
92 
94 
96 
98 
•CO' 


81 
82 
83 

be 

i8t 


87 

38 

9( 


iu2 
104 
lOf 
I(J& 
1  10 
1  12 
lU 
I  16 
I  i8 
i2r 
12:0 
124 
i26 
128 


1  84 
.36 
38 
14* 

:42 

144 
146 

i  4& 

I  50 
li>2 
'54 
1  5  6 
!58 
16t 
162 

i  C)t 

!  Gt 

6cS 

.70 

I  72 

i  "^  ^ 

i  70 
.77 
'.'?9 
t  H.2 


In-. 


o 

15 

'  7 
18 

19 

--:(•■ 

2. 

■w  3 
2  4 
--  5 
2t. 
2  / 
27 
■-9 
30 
21 
32 
00 
34 
S5 
36 
37 
)3 
39 
40 
4> 
•*2 
43 
43 
45 
46 
47 


30 
32 
34 
36 
3£ 
4C 
421 
44 
47 
49 
5  1 
53 
55 
37 
&(^ 
62 
64 
66 
68 
70 
72 
74 
77 
78 
81 
83 
85 
87 
89 
9; 
9  5 
95 
98 
100 


lot 
I  !( 
112 
I  15 
11?! 
56  1  19 


D  i 

5  2 
53 
5 

55  i 


48j:u'2 
49  :04 


o  ( 

58 
59 
60 
61 
62 
63 

6  4 
^O 
;  6 
67 
08 
69 
70^ 
71 

7  X 
73 
7- 
75 

-6 

77 
78 

79 
80 
81 
82 
tt3 
8^ 
35 
8^ 
87 
08 
■si, 
90 

95 

f 


121 
123 

127 
i29 

132 

,-., 

;36 

i3!: 
14( 
142 
4', 
46 
149 
15! 
I  5  J 
■  5, 
15V 
159 
161 
1.64 
166 

;  6 

70 
.72 

i74 

•  7  6 

.78 

181 

i83i 

i85| 

'i87| 

i89.j 

\9:l 


CO 


A  TABLE  OF  SQUARE  TIMBER, 


81206 

pjeosi 

83;919 

111  P4J^:22 

113  8r.i2'24 


:^:^||44nCfr!227| 


111  1231^ 

50:125  ,j  23c!p0 


l5^"'|9l|24Cf 
132i9^j^42^. 


Oi 


OF  THE  WEIGHT  AND  DLMEiNSIONS 
OF  BALLS. 

TROBLEM  I. 

To  Jiiid  the  Weight  of  an  Iron  Ball,  from  its  Diameter. 

An  iron  ball  of  4  inches  diameter  neighs  9ros.  and  the 
weights  being  as  the  cubes  of  the  diameter!!,  it  mil  be,  as 
64  (which  is  the  cube  of  4)  is  to  9  its  weight,  so  is  the 
cube  of  tfre  diameter  of  an  J  ball,  to  its  v.eight.  Or,  take* 
^^  of  the  cube  of  the  diameter,  for  the  weight.  Or,  take  -^ 
ot  the  cube  of  the  diameter,  and  |  of  that  again,  and  add 
the  two  together,  for  the  weight. 

EXAMPLES. 

1. 'The  diameter  of  an  iron  shot  being  6-7  inches,  re- 
quired its  weight  ?  Ans.  42-294lb. 

2.  What  is  the  weight  of  an  iron  ball,  whose  diameter  is 
5*54  idches  ?  Ans»  24ib.  nearly. 

PROBLEM    II. 

To  find  the  Weight  of  a  Leaden  Ball. 

A  leaden  ball  of  1  inch  diameter  weigh?  -f^  of  a  pound  , 
therefore  aa^  the  cube  ot  1  i.*  to  -^-^  or  as  14  is  to  3,  so  is 
the  cube  of'ihe  diameter  of  the  leaden  ball,  to  its  weight.— 
Or,  take  ^  of  the  cube  of  the  diameter,  for  the  weight, 
oearly. 

EXAMPLES. 

1.  Required  the  weight  of  a  leaden  ball  of  6*6  inches 
diamett-r  ?  Ans.  61-6061b. 

2.  Wliat  is  the  weight  of  a  leaden  ball  of  5-30  inches 
diameter  ?  Ani.  32lb.  nearly. 

PROBLEM    III. 

To  find  the  Diameter  of  an  Irom  Ball. 

Multiply  the  weight  by  7^,  and  the  cube  root  of  the 
product  ivill  be  the  diameter. 

F 


62  A  TABLE  OF  ROUyO  TIMBER. 

ExASTrLC.  What  is  the  diameter  of  a  24lb.  ball  ? 

Ans.  5'54  incbe«, 

PROBLEM    IV. 

To  Jind  the  Diameter  of  a  Leaden  Ball, 

Mnhiply  the  weight  by  14,  and  divide  the  product  by  *> : 
iheQ  the  cube  root  ot  the  quotient  will  be  the  diameter. 

Ex..:.-  „z,  Vv'hat  is  the  diameter  of  an  8Ib  leaden  ball  ? 

Ads.  3-343  inches. 


A  TABLE  OF  SOLID  MEASURE,  OF 
ROU>'D  TLMBER. 

By  the  following  Table  the  solid  contents  of  any  stick  of 
round  timber  may  be  found  at  sight,  from  6  inches  to  40 
inches  in  diameter,  and  from  7  feet  to  91  feet  in  length.  It 
rises  1  inch  in  niaxe  er  at  a  time,  and  one  foot  in  length  at  a 
time.  The  let't  hand  columns  of  each  page,  and  the  col- 
umns at  the  right  hand  of  each  double  line,  give  the  inches 
in  diameter,  and  the  other  columns  the  contents,  which 
ure  given  in  cubic  feet  and  tenths  of  a  foot.  Over  the  top 
of  these  two  columns  is  placed  the  len2;th  of  the  stick  ;  and 
to  find  the  contents  of  any  stick,  first  tind  the  length  at  the 
top,  then  the  inches  in  diameter  in  the  leit  hand  column,  and 
ugainst  this,  to  the  right  hand,  will  be  fonnd  the  content* 
sought  for,  in  cubic  feet  and  tenths  of  a  foot,  f'or  exam- 
ple:  to  tind  the  number  of  cubic  feet,  which  a  stick  con- 
tains, that  is  7  feet  in  length,  and  10  inches  in  diameter — 
tirst  tind  7  feet  at  the  top,  then  follow  the  let't  hand  column 
down  to  10  ;  then  against  10  to  the  right  hand  will  be  foand 
3  feet  aad  8  tenths  of  a  feot. 


A  TABLE  GF  SQUARE  TIMBER. 


!  cr? 

pi?0|51 
Ins.)  50 

1!?: 

141 

144 

147! 
150| 
153 

Sid 

0 
1 

51 

52 
-  0 
00 

54 

65 

149; 
152^ 
154 
157 
I6O 

Sic 

0 

eSlj 

In?.' 

j 

C 
c 

-.3 
54 

55 

156 
159 

1621 
165 
168 

Sid 

c" 
a. 

las. 

0 

51 

52 
53 
54 
55 

1631 

iDij 

1701 
1731 
i76j 

14 

39  56, 

155| 

H 

44 

56 

163^ 

u 

~[3 

56 

1711 

14 

'^''^56 

IGGJ 

16 

41  57 

15[i\ 

15 

57 

166: 

1  -, 

4r. 

57 

174 

15 

48 

57 

183 

16 

44^ 

58 

161  16 

46 

58 

I69i 

16 

49 

58 

177 

16 

51 

58 

186 

17 

47 

59 

I(':  i 

17 

49 

59 

172: 

1  / 

52 

59 

180 

17 

51 

'•9 

189 

18 

50 

60 

166 

18 

52 

60 

175| 

18 

55 

i'( 

184 

18 

58 

oO 

192i 

19 

53 

61 

169 

19 

55 

■31 

178; 

19 

58 

61 

187| 

19 

61 

61 

196 

20 

65 

62 

172 

20 

58 

62 

I8I; 

20 

61. 

62 

190 

20 

64 

62 

199 

121 

58 

63 

175 

21 

61 

63 

184: 

21 

64 

63 

193' 

21 

67 

63 

202 

■22 

Ql 

G4 

178 

22 

64 

64 

187 

22 

67 

64 

196 

22 

70 

64 

205 

23 

64 

65 

180 

23 

67 

65 

289 

23 

70 

00 

199; 

23 

74 

65 

208 

24 

66 

66 

183 

?4 

■70 

G6 

192! 

24 

73 

66 

202 

24 

77 

66 

212j 

{25 

69 

67 

186 

25 

73 

67 

195i 

25 

76 

67 

205 

■0  5 

80 

61 

215i 

l26 

72 

68 

i8C 

26 

76 

68 

198! 

26 

79 

68 

208 

26 

83 

68 

218] 

27 

75 

69 

191 

27 

79 

69 

201| 

27 

82 

69 

211 

X'7 

86 

69 

221 

28 

78 
80 

70 

194 

28 

81 

70 

204. 

,0 

86 

70 

214 

28 

90 

70 

224 

29 

71 

197 

29 

34 

71 

207| 

29 

89 

71 

217 

29 

93 

71 

228 

30 

83 

72 

200 

30 

87 

72 

2101 

30 

92 

72 

220 

3G 

96 

72 

231 

31 

86 

73 

203j 

31 

90 

73 

213! 

31 

95 

73 

223 

31 

99 

73 

2341 
237j 

32 

89 

■74 

2051 

32 

93 

74 

216 

32 

98 

74 

226 

32 

102 

74 

33 

91 

75 

2081 

33 

96 

75 

219 

33 

101 

75 

229 

33 

106 

75 

241} 

34 

94 

76 

211! 

34 

99 

76 

322 

34 

104 

76 

233 

34 

109 

76 

244i 

j35 

97 

77 

214: 

35 

102 

77 

224' 

35 

107 

77 

236] 

35 

112 

77 

247| 

|3€> 

100 

78 

216| 

36 

105 

78 

227 

36 

110 

78 

239 

36 

115 

78 

250 

37 

103 

79 

219; 

37 

108 

79 

230 

37 

113 

79 

242 

37 

119 

69 

263i 

38 

105 

80 

222 

38 

111 

80 

2331 

38 

116 

80 

245 

38 

122 

80 

257 

39 

108 

81 

225 

39 

114 

81 

236 1 

39 

119 

81 

248 

39 

125 

81 

260 

40 

111 

82 

228 

40 

116 

82 

239 

40 

122 

82 

251 

40 

128 

82 

263 

41 

114 

83 

230' 

41 

119 

83 

242 

41 

125 

83 

254 

41 

131 

83 

266 

42 

116 

84 

233 

42 

122 

84 

245 

43 

128 

84 

257 

42 

135 

84 

269 

43 

119 

85 

236 

43 

125 

35 

248 

43 

131 

85 

260 

43 

138 

85 

273 

44 

122 

86 

239 

44 

128 

86 

251 

44 

135 

86 

263 

44 

141 

86 

276 

45 

125 

87 

241 

25 

131 

87 

254 

45 

138 

87 

266 

45 

244 

87 

279 

46 

128 

88 

244 

46 

134 

88 

257 

46 

141 

88 

269 

46 

147 

88 

282 

47 

J  30 

89 

247 

47 

137 

89 

260 

47 

144 

89 

272 

47 

150 

79 

286 

i48 

133 

90 

250 

48 

140 

90 

262 

48 

147 

90 

275 

48 

154 

90 

289 

!49 

136 

91 

253 

49 

143 

91 

265 

49 

150 

91 

278 

49 

157 

91 

292 

i50 

139 

92 

155i 

50 

146.92 

268 

50 

153 

92 

282 

50 

160 

92 

♦95 

G4 


A  TABLE  OF  sqUARE  TIMBER 


,— lIas.5o!i-5 

63|l78: 

o     54  181 


=  14 

!l5 

;17 
!l8 

:i9 

i21 

24 

;2C 
'27' 
i^8 
39 


4/ 

50 
54 
5 


56 


ot 


185 
188 
191 
58|l95 
59|198 
60!6C  202 


64 
67 

70 


77 
80 
84 
87 
91 
94 
9 


Id* 

§      § 

14    49 
o 


51  179!'5ide  23 
50:1331;  _lln? 


53^18b[[  -J  ^ 
54.I90I1  §1  I' 


55!l93t 


61  203 


621208 
63!212 
7464|215 
65|213 
66i222 
671225 


68J228 
691232' 
701235 


115 
il6 

|l8 
|19| 
|20 
21I 
J22 
j23 
|24 
125 
26 


56 
6(i 
C3 
67 
70 
74 
77 
81 
84 
88 
91 


561197:  14| 
5720015 


51 


1911  -^i 

194  q 

54  198J§ 


51 


;.2u4 
59:207 
60' 211 
61  214 
62218 
63i221 


.-I 


16 
17 
18 
19 
20 
121 


52 
53 


187.;Sidf 


Ins.  52 


bo  57  209. 


62 

66 
70 
73 
77 


64,225il22i  81 
65,226  23|  84 
D6|232!!24i  28 
67i235:[25i  92 
68'239i  26    95 


27    95  691243 


71123812 


28 


:« 


30  lOi 

3lil04l 

:32iI07 

-3'5!l  1  t 
•■-'Oj  I  1  i 

•34ill4 
1251117 

;36|l2l 
137  U  4 
♦38  127 
;3S  13' 

J4o|i.: 

'411137 
'!2;i41 
13  144' 
:44il48 


721242 

r  0^245 

74;248 
-5!252 


130 


98 
102 
lOol 


7C;255 
77259 


ol|109 

3-.n2 

;33ilC 
■34!ll9 
!35|123 

^^•'l26 

:43r. 

801269  :38[l33 


701246! 


27}  99 
28il0S 


71  249i[29|l06 

72i253j'S0'llO 

!256l31  114 

32Jil7 

75'263i!33  121 
-.1 


I' 
60 

61J224 

62228! 

631231 

64  235 


55'202  j_i 
561205  !14 
lo 
69158  213 
o9 
220' 


16 
17 
18 
19 
20 
21 
22 


01 
61 
65 

69 

*.  £~* 
I   ^ 

76 
80 
84 


65  239 

661242  24! 
67|246  -5! 
682501261 
691253,1:7' 
■Gl257;;:r 
7]i26i;::: 
264;Soi 
268:31 


23^51!  196 

199. 

00  203 

541207' 
3^211 
561215 
o/i219 
o8[222; 
9226i 
60]  250 
61;2S4 


62 
00 
64 


88  65 


92 
96 


9968 


267!i34!l25l76|279:!34 


77l27r 


72 
73 
74 
75i27o  ioo 


103 
107 
111 
U5 

iir 
122 

126 
130 


238; 
24l! 
245- 
2,9| 
253^ 
257^ 
261! 


69  264^ 
701268! 
7I|272| 
72  276; 

280! 

284; 

I 


83j27j^  j41] 


151 

154  >'■ 
1 


41J144 

:147 

151 

.  154 

15 

161 


351128  77 
78  274ll36!l32:£ 
79i2:7'37:136 
80  2811  3CM3' 


85j291|.4ljloOJc;3j305:j41 

gj;  ,-  ,-^   1-  V-   ;       ,   r   '  ■;. 

Or. 


8t 


1*^  291! 

-  -  :95i 

To  299; 

I42|79iS03i 

:07: 

10 

•14, 


5718. 


3j318: 


818' 


8r 


3t.>:  i6CJi}2|309 


,    ._,   .  iI80-31J334,li9 

l^lJTG  j2-323;|50h&3  92  337  |50 


188I91J349! 
192'92i352' 


A  TABLE  OF  SqUARB  TIMBER. 


65 


51 1^221  !Side25| 
Ins 


56!243il4 
57|247J15 
58|252||l6 
59:256j!l7 
60i260  18 


o 


61j265i 

G.2|^69 


19 
20 
21 

641278  29 

6rl282l;23 
66 


63 
67 
72 
77 
81 
86 

Q 


108  67 
113)68 
117169 

C 

71 

-o 


jSS  152  80 
139|l  58  81 
.40[i60|82 
:41 1164103 
J42|l68  84 
|43|l72  85 
i44'l76!86 
145  18o!37 


28J121 

-^9  120 

30|13C; 

-^.,3l|i34 

308|'32!i3G 
3l3'!33{i43 
3l7;i34;i47 

•321j35!i52 
325136  156 
329i37'j60 
38165 


8g!333 

31  337 


328 j|40|l 66  8:|342 


332:!41 
33ej|42 

"44 


0IJ43 

344! 


175 

179 
183 


--,-  348ij45!l87 
146  184  88!552'j46|l92 
|47  188  89  35t  147  196 


95 

99 

104 


51  230! 
52 


54 


56 


o9 
60 
61 


286l|2^  108 
29ri25Jll3 
295i;26jll7 
299|j^7!l22, 
304'j28|l26 
308:'29!l3l 
3l2i;30jl35 
73i3l7{i3]|14C 
32II44 


00 
64 

>^' 
6C 
67 
68 
69 


339; 

2441 
248! 
253I 
257} 
262[ 
266! 
-^71! 
275i 
B8C! 


74i32i: 


75|325J 
76|53oJ 


771234113; 


149 
153 

158 

78!33pjl3c!i62 
79j343;!37|i67 
,  ..      .,,--,171 

39)169  81J35]|3c.h76J81 

40i  1 73  82j35f.|Lic'  ]  80  82 


284 
28£ 
29? 
298 
302 
30": 
311! 

7013161 

71 

72 


320i 

32  £( 

73  329^ 


77 
78 
79 
SO 


178  83J3e0|'41 

182  84i364|j42 


|48 
149 
'50 


192190 
196bl 
200i92 


36( 

36 

36» 


48 
49 

50 


04 


3381 

34vf 

35n 

5(| 
36 1 1 
3'6f  j 
3711 
37^ 


lS6j85j369i43J194i8ci88.i 
19P8ej373lU4|l98i06|38( 


185  83 
189|3-i37^ 


87 
88 

ftO 


377|i45!203[87|39: 
382Ji4Gi207 
38e!|47i2i2  8; 
390J;48i2I7 
39o|i49J221 


n7  92!399|;50i?26 


08139^ 

I  105 

X-!40{ 

91141} 
92141: 


A  TABLE  or  SQUARE  TIMBER, 


iJecij^  51. 248  f^^^e '27151  c258,  5i^^-^5|51  -•: 


-M.l>: 


f^f  = 


i-i 
}  5 

i  I 


54[ 

5' 

05166 


-'   -. 


i^H 


rO; 


53i 

5f 

re- 


el 

06 


I;i5 


-K.        ^ 


i  -4, 
:-5 


17! 
ir>' 


*  d 


94  xV:-^   91    ;?0 

0So5:  05  ^3| 
13|66.   10  24; 

to!  £:>^  2c 

71:     5-      2V 


92 


61 


5 

59 

64 


.  o  ■*  -  o  1 
7-4  47  32 
75    52  33' 


77;  Cl  ;35 


12 
17 
2? 

o- 

31 

41 
4^' 
51 
5t 
61 
6^^ 
70 


521  o3\  ^1 

34!63jli 


^1 1^-52    63:;  -    Ini 


00! 

56, 

57, 


63 


71 


I  O  1  1  -I  f 

7  c   151   7''" 

83;iei  81 
8c  17i  86 
93  l&l  91 
97   l&l  96 


53!  68! f  -: 53S  78- 

54!  73^11  ?    5J[  83- 

55  78j|_l_!  I     35    89j 

5C  83  14i^.>'i6|  94i 

57  88!!l5|  7-57'  991 


59  98ilni  8-|^9[jO 

60  30-  "   ^'^' 


o.i  12;22}   11 

j5i  17>23|   16 

-36!  22  1:24    21 

7!  27  2ol   26 


31  :^6; 


3'-   - ' ;  01 


T?:  41   28i  42 

7r 


i  o 

74 


4^:*   29;  47 

51  30'  52 

31  5: 
3 


- 


61 

70 
<  o 


93.  1 61  31 


-o 


>8  304[ 


61 1  0. 


62t302  20I1OI62  14[J20'  o5o2| 

3^  07-21J  0663  19r2l|   i063; 

|t4|  24'!22'  i5|64    36J 

t'o'.  29'.  25;   o] 

■36|  oJ;*24;   oe 

oi  ocS-c     31 

r        ^ 

3^ 


o2i 


-X:a 


00 

66 
67 

6Si  57[ 
J9|  62[ 
70f  67; 
71 1  731 
72!  64:'3ei  57J72|  78| 
73?    t3; 


70i   54i'2L|  47 


311  G5 


18J30: 


«4 


9?'   it 


2!  62  74    75f|32  e-'^-    ^^ 

35'  67  75}  80,;33j  75""    ^^ 

34I  7276f  Sc\\3^l  7b 

77!77i   9C'l35|  8^ 

'     ■         3i3Gi  8' 

-'!^-i94 

92t£0:  05i>38i  9C» 


00 


''   15 
20 
25! 
30i 


41 
4€j 


75    94 
7«^I  991 
67J404- 
78    09| 
70!  151 

3c(  21  r 


-'  30| 


-ill  S2I. 


441  06  S6[403  44 
45    11  -'    ""      - 

ioj  iti: 

47t  2ii 


4  3 


x\\3\  05  *l;  03{<J3|  2tH41|  isissj  35j 
U.^   1^.44?  2?(86i  35f|4J.   31 

ir87!  ':■   "    :      '    '"  '*!  3^ 


34  4  7 


;:    i9  8 

3li92|  32n50;  44b21  49£5us  dc 


3f 

-   i  4! 

47i  4- 


'>0 

91  j  78j 
92}  65  f.5Ci|  62I95I  82f 


40 
46 
51 
57! 


08!  621 

s9;  -^^ 


671 
72. 


A  TABLE  OF  SqUARE  TIMBER. 


^fue  2\j 

51 

277.S:de-^H>| 

j\' 

288 

bid 

e29j51 

298 

Sid 

e29^»51 

3C8 

~'  IU5. 

52j 

83 

<rr 

las. 

52 

93 

~z 

_Ius.5o 

304 

■^^ 

Ins.  52 

14 

=  ,'    o 
7;  1  5_ 

I--I   76 

53 
54 
55 

56 

89 
94 

99 

i 

p 
~79 

53 
54 
55 

56 

99 

534 

10 

le 

14 

0 
0 

.~f- 

00 

54 

09 
15 

21 
27 

* 

3 
J. 

53I 
54 
00 

20 
26 
32 
38 

305  ;14 

82  56 

14 

"85)56 

U     82 

57 

*10ll5 

85 

57 

21 

15 

88  57 

33 

15 

90!57 

44 

16    87 

58 

15 

16 

90 

58 

27 

16 

93  58 

39 

!1C 

97158 

50 

17    93 

59 

2r 

17 

96 

50 

32 

17 

99,59 

44 

Il7 

103:59 

56 

18 

98 

60 

27 

18 

101 

60 

38 

18 

105160 

50 

lie 

09  60 

62 

19 

103 

61 

32 

19 

07 

31 

44 

19 

11 

61 

56 

19 

1561 

69 

20 

09 

62 

0^ 

20 

13 

32 

49 

120 

17 

G2 

62 

20 

2162 

75 

21 

15 

bo 

.43 

21 

18 

63 

53 

21 

22 

53 

68 

21 

27 

63 

81 

22 

20 

64 

48 

22 

24 

34 

61 

22 

28 

34 

74 

22 

00 

64 

87 

23 

25 

65 

54 

0^ 

3C 

35 

67 

|23 

34 

65 

7C 

j23 

39 

60 

'  93 

9  J 

31 

GG 

59 

24 

35 

06 

72 

;24 

40 

36 

85 

j24 

45 

GG 

99 

25 

op 

67 

G5 

25 

41 

37 

78 

25 

46 

0  < 

91 

!25 

51 

67 

405 

26 

42 

68 

70 

2C 

47 

-0 

83 

,26 

52 

38 

97ii26 

57 

68 

\  11 

27 

47 

G9 

75 

27 

50 
0^ 

89 

89 

I27 

58 

39 

403 

r>  — 

63 

69 

17 

j2& 

52 

70 

81 

00 

^0 

58 

70 

95 

128 

GA 

70 

09 

28 

69 

70 

23 

129'   58 

71 

86 

29 

63 

71 

400 

!29 

6f 

71 

15 

00 

75 

71 

29 

j3u    63 

72 

92 

30 

69 

72 

03 

■30 

75 

7  w 

20 

30 

81 

72 

35 

■31    69 

73 

97 

31 

75 

10 

12; 

;3i 

81 

73 

26 

31 

87 

73 

41 

132  j  74 

74 

403 

32 

80 

74 

17 

139 

87 

74 

32 

32 

93 

74 

47 

1331  8C 

75 

08 

33 

86 

75 

23, 

33 

'b 

38 

■33 

G£- 

76 

63 

J24i  85 

76 

14 

i34 

92 

76 

29! 

134 

9f 

76 

44 

:34 

2<.j5 

76 

69 

35I   91 

77 

19 

35 

97 

77 

34' 

!35 

204 

77 

50 

|35 

11 

77 

6b 

,36;   96 

78 

25 

1 36 

203 

78 

40J 

SC- 

K 

(O 

55Ji36 

H 

71 

■37-201 

79 

30 

'137 

09 

79 

45 

SI 

16 

70 

1  KJ 

61 

37 

24 

79 

77 

•38!  U7 

80 

35 

i38 

14 

80 

51 

38 

80 

67 

38 

30 

80 

83 

■39!    12 

81 

4i;i39 

20 

81 

39 

,  2a|8i 

73 

!39 

35 

81 

89 

UOJ   18 

82 

46i!40 

25 

82 

62 

40 

33  82 

79  }40 

42 

82 

95 

i^V.  23 

83 

52||41 
57;  42 

31 

83 

G8 

41 

39JC3 

85i|41 

48 

83 

501 

■42|   2? 

84 

37 

84 

74 

42 

45|84 
51185 

91 

42 

6484 

07 

43|  34 

85 

63|  43 

42 

85 

79 

43 

96  l4S 

5085 

13 

;44|  39 

86 

68 

44 

48 

36 

85 

44 

63|87 

502jJ44 
08.46 

CC86 

20 

:45!  45 

87 

74 

4- 

54 

87 

90 

45 

72  s  7 

25 

.1=3 1   5C 

88 

79 

4C 

59 

88 

•  96 

46 

67  Sij 

14'  43 

78  88 

32 

r    ot 

89 

85 

47 

6r. 

89 

302 

47 
|48 
49 
|50 

74 

Of: 

20|  47 

84  89 

38 

4';,   64 

GO 

9o; 

48 

70 

90 

07 

0/ 

30 

251148 

90 

on 

44 

'49j   C: 

91 

95 

49 

76 

91 

13 

86 

.'1 

31.1 

49 

96 

91 

50 

M    '^ 

92 

301    :50 

82 

92 

18 

92 

32 

37! 

50 

302 

92 

66 

A  TABLE  OF  ROUXD  TIMBER. 


GS 


c 

7  Fl. 

S-' 

8  Ft. 

">-»• 

9Ft.!!P10Ft.i?>llFt.    , 

1 

v. 

Lons:. 

ft- 

X 

6 

Lonff. 

1 

G 

Lod; 

^! 

- 

Lon 

"     1 

^ 

Lons:, 

o 

3E 

O 
o 

1 

6 

9 

OB 

O 
o 

3 
^^ 
O 

1 

6 

O 
o 

9 

ST 

G 

1 

4 

1 

8! 

6 

2 

Oj 

2      1 

7 

1 

8 

7 

2 

1 

4 

2 

4l 

7 

2 

7 

7 

2     9 

8 

2 

4 

8 

2 

8 

8 

3 

1 

8 

3 

5 

8 

3     8 

9 

3 

1 

9 

5 

9 

o 

9 

1 

9 

4 

4 

o 

4     8 

10 

3 

8 

10 

4 

10 

4 

Q. 

10 

5 

41 

10 

6     0 

ii;    4 

6 

11 

5 

3 

11 

5 

9 

11 

6 

6 

11 

7     4 

12:     5 

5,12 

6 

3ji2 

7 

1 

12 

7 

8 

112 

8     6     • 

131     6 

4 

!^? 

7 

^i 

13 

8 

5|!l3 

9 

4 

113 

10    0    . 

14!      7 

5 

u 

8 

^ 

14 

9 

6 

14 

10 

6 

14 

11      7     1 

loi      8 

6J15 
7116 

9 

8il5 

11 

l! 

15 

12 

4 

15 

13     6     ! 

IC 

9 

11 

2 

16 

12 

6i 

16 

14 

o; 

16 

15     3 

17 

11 

0 

17 

12 

6 

17 

14 

l; 

17 

15 

7: 

17 

17     3 

18 

12 

3il8 

14 

1 

18 

15 

9l 

1 

18 

17 

7 

18 

19     4 

IC^ 

13 

7;|i9 

15 

7 

19 

17 

7| 

19 

19 

■'i 

19 

21      6 

20 

45 

3-;2o 

17 

5 

20 

19 

6i|2C 

21 

6; 

20 

23     9 

21 

16 

"i'^ 

19 

2 

21 

21 

5}|2} 

,23 

8; 

121 

26     3    i 

22 

18 

4^f22 

21 

0 

PO 

i  23 

61122 

126 

3 

22   28     8     , 
23f3l      5     i 

23 

20 

2;  23 

22 

9 

23 

\  25 

'~    ^'■"- 

-^  .-k 

'~- 

24 

21 

8J24 

25 

Oi:24 

■  23 

24   35     3     J 

25 

23 

7 

25 

27 

2j25 

|30 

7ji25 

:  34 

ui 

125  37     3     ■ 

26 

25 

7 

26 

29 

4;!2C 

!32 

lib 

e! 

!26   40     4 

27 

27 

6|i27 

31 

6 

27 

6(;27 

39 

|27   43     2 

28 

29 

7=28 

33 

^ 

128 

^  38 

4:i28i  42 

o 

28   46     6     ' 

29 

31 

8 

i29 

36 

3 

oc 

i  41 

Ol  29,  45 
9  30  49 

'^1 

29   50     0 

30 

34 

o 

J30 

39 

0 

30 

i  43 

0" 

^30   53     5 

ol 

36 

6 

h 

41 

8 

31 

47 

0  31 

52 

**- 

|31 

57     2* 

32 

38 

9 

32 

44 

5 

32 

52 

2  32 

55 

6 

|32 

61     2    i 

>3 

41 

4 

33 

47 

Q 

33 

53 

3  33 

59 

1 

33 

65     0 

34 

43 

7  34 

50 

3 

34 

oQ 

Si!34 

8!b.5 

82 

9 

34 

C9     0 

o  - 

46 

5  35 

53 

0 

JO 

59 

^^ 

5 

Sai^r-^ 

36 

49 

2!:3G 

oQ 

0 

136 

63 

2:iSt 

70 

5 

136   79     0~^ 

37 

52 

0'j37 

59 

4 

37 

67 

0  37 

74 

5 

;S7   81      3    X 

38 

54 

1 

38 

Q2 

f 

38 

70 

6  3( 

78 

8 

iSS   86     ? 

39 

57 

8 

39 

&Q 

74 

4  3S! 

83 

3i 

b^  91    '. 

:o 

60 

8!40 

69 

e;;4o 

78 

oi'40 

87 

3l 

!4(    '^b     7     , 

A  TABLE  OF  ROUND  TIMBER. 


68 


V— ' 

12  Ft. 

— 1 

13Ft.i^ 

14  Ft 

?;i5Ft!  glGFt 

5 
ft 

It 

6 

Lor.2-. 

-i 
a. 

6 

Long. 

1  =; 

s 

ft 
6 

Long. 

i| 

;  re 

!  0 

1  J^ 

i 

1  6 

Lonj 

.  0 
0 

3 

en 

y. 

re 

f 

6 

Loni 

0 
0 

D 

re 

EJ 

r. 

6 

o 

0 
0 

*  0 

n 
0 

2     5 

2 

5| 

2 

7 

2 

~9 

0 

T 

7 

3     2 

7 

3 

5 

7 

3 

7 

7 

4 

0 

7 

4 

2 

8 

4     2 

8 

4 

5 

8 

4 

8 

8 

5 

2 

8 

5 

5 

9 

5     Sj 

9 

5 

7 

9 

6 

1 

!  9 

6 

6 

9 

7 

0 

10 

6     5 

10 

7 

1 

10 

7 

6 

10 

8 

1 

10 

8 

7 

li 

7     9 

11 

8 

6 

11 

9 

3 

11 

9 

8 

11 

10 

5 

12 

9     4« 

12 

10 

2 

12 

11 

G 

j12 

n 

8 

12 

12 

1 

5 

13 

11      1 

13 

11 

9   13 

12 

8 

il3 

13 

8 

13 

1    14 

6 

14 

12     8 

14 

13 

9   14 

14 

9 

114 

16 

0 

141    17 

0 

15 

14     9 

15 

-J  6 

1    15 

17 

2 

|15'   18 

5 

15     19 

7 

16 

16     8 

16 

18 

2'  16     19 

5 

'AS    ^ 

8 

16'  22 

0 
0 

17 

18     9 

17 

20 

4 

17j   21 

8 

'17:  23 

5 

17;   25 

0 

18 

21-    3 

18 

22 

8 

18    24 

^ 

^ 

|18|  26 

4 

18'  28 

2 

19 

23     6 

19 

25 

5 

19!   27 

3i 

:i9^  29 

0 

19 

i   31 

3 

20 

26     2 

20 

28 

2 

20i  30 

3 

'20:  32 

5 

20 

o4 

6 

21 

28     7 

21 

31 

0 

2li  33 

3 

21    35 

8 

21 

38 

1 

22 

31      5 

22 

34 

0 

22I   36 

6 

\qq 

39 

0 

22 

41 

$ 

23 

34     5 

23 

37 

3 

23!   40 

2 

!23 

42 

0 

23!   45 

7 

24 

37     6 

24 

40 

6 

24    43 

6 

124 

46 

7 

24 

49 

6 

25 

40     7 

^'5 

44 

0 

25    47 

4 

25    50 

7 

25 

53 

9 

26 

44     0 

26 

47 

7 

26    51 

3 

|26;  54 

8! 

26 

58 

3 

27 

47     4 

27 

51 

0 

27;   55 

0 

27;  58 

9 

27 

63 

0 

28 

51      0 

28 

55 

2 

28    59 

0 

i28'  63 

5 

28 

67 

6 

29 

54     5 

29 

58 

c 

29;   63 

4 

!29'  68 

0 

29     72 

4 

30 

58     4 

30 

63 

4 

30 j   68 

0 

bo    73 

3 

30j   77 

7 

31 

62     5 

31 

67 

7 

31     72 

7 

i31 

78 

p 

31     83 

0 
0 

32 

Qo     7 

3? 

72 

4 

32 

77 

5 

3: 

83 

5 

32 

83 

7 

33 

71     0 

33 

76 

8|33 

82 

5 

S3 

88 

6 

3. -5 

94 

5 

M 

75     3 

•"-•4 

81 

4 

34 

87 

6 

94 

3 

3. 

99 

6 

35 

79     8 

3.5 

06 

4 

35 

92 

!35 

99 

5 

35 

iC6 

8 

36 

84     4 

3'. 

91 

3  \3r 

£=8 

0 

136 

105 

5 

36 

112 

9 

37 

09     5; 

37 

96 

n 

0 

37 

104 

7 

i37JlI2 

0 

37 

1  19 

5 

38 

94     41 

99     3i 

08 

i02 

i 

3? 

no 

0 

|38!117 

< 

:-:8 

126 

0 

39 

39 

108 

3 

0 ', 

116 

9 

124, 

39 

132 

8 

'0 

101     4l 

i'iO 

113 

^1 

i40 

124 

0 

140 

130 

r 

4u 

139 

5 

J  TABLE  OF  ROi'XD  TIMBER. 


.  ir.i 

17  Ft.! 

i^l8F 

t.' 

"w, 

19  Ft. 

^\ 

2uFt.i|5  21  l^Tl 

*  =  1 

5  5 

Lone. 

O 
o 

h 

7. 

6, 

Loiir, 

! 

r 

Lon... 

X 

Loi-g 
O 

hi!  Lon^.    \ 

;  S  i 

o 

_ 

)  ■ 
1 ' 

1 

^"^i 

o       oi 

3 

3             ', 

<:•! 

3 

j 

4       11 

,  ri    4    5 

i 

4 

8; 

(■  ' 

5        'ii    ' 

5 

7 

5      6 

'  8; 

5     ?! 

' 

f 

-  i 

b 

b 

6      ^i 

&i 

7 

0 

8 

7      3| 

i  9^ 

7      5i 

1 

o 

u 

-^ 

8      4 

9 

8 

8 

^ 

9      4 

iiO       9      3J 

!|o 

9 

8 

^  0 

10     4 

iO 

11 

G 

10 

11      5 

11 

11      2 

i  1- 

11 

9 

i  ! 

12      e 

n 

13 

3 

\  1 

13     9 

12 

13     4 

u 

14 

2 

12 

15      0 

i2 

15 

^ 

42 

16     6 

13 

17     7 

\3     16 

I 

3- 

ir;  f 

i  o 

18 

5     .o 

19      5 

14' 

18      3 

u;  19 

3 

14' 

20      7 

14 

21 

4     i4 

22      5 

15;    21       1 

22 

■5^ 

23      t, 

.5 

24 

7  jl5 

,26     2 

16    23      8 

t 

25 

2 

16| 

26      7 

16 

28 

2|  16 

29      5 

17,   26      8 

w 

28 

3 

'7| 

30     <J 
35      6 

!7 

31 

6!  17 

53     3 

18    50      1 

18 

31 

9 

lo* 

18 

55 

4|8 

37     2 

19    33      5" 

f^ 

r35 

4 

19 

37     5 

19 

39 

4  jlV 

41      5 

20    37      2 

20 

39 

2 

20 

41      5 

20 

43 

7 

20 

46     0 

21     40      9 

21 

43 

1 

21 

45      ' 

2  ! 

48 

4 

21 

50      4 

2^1  44      7 

2ii 

47 

4 

22 

50      2 

■22 

i    52 

7 

-22 

55      2 

23 

49       1 

23 

51 

8 

23 

54      8 

23 

:   57 

7 

23 

60      8 

24 

5o       o 

2-i 

56 

1 

24 

59      5 

24 

62 

9  'i24 

66      2 

35 

57     7 

25 

61 

4 

25 

64      8 

25 

i   68 

e 
O 

i26'   71      8 

?6 

62      6 

-26 

65 

4 

26 

70      2 

26 

1   74 

0 

26j    77      6 

27 

67      5 

27 

'   71 

5 

27 

75      4j;27 

|79 

5 

27!   85      5 

28 

72      6 

28 

i  ^^ 

2 

28 

81      5|r28 

i    85 

e 

28 

1   90      0' 

■19 

77     7 

29 

\   82 

4 

29 

87     2 

29 

i   91 

511--.Q 

96      5 

30 

83      5 

30 

88 

4 

30 

93      5 

SO 

i   98 

5 

30 

103      4 

31 

89      4 

31 

94 

5 

31 

1   99      5 

31 

•105 

s 

31 

HI      0 

32 

95      5 

32 

jlOl 

0 

32 

il06      8 

32 

;il2 

4 

32 

1  18      0 

33 

101      5 

|107 

o 
O 

38 

1  15      4 

119 

5 

3b 

125      4 

34 

107      ^ 

34 

113 

8 

34 

120     0 

34 

il26 

7  |34 

135      0 

35 

114      0 

S5;i2© 

5 

35 

127      2 

35 

|135 

0|35 

141      0 

,36 

120      6 

36'127 

5 

36 

135     C 

36 

5142 

2] 

'3f- 

U9.    C 

37 

127      6 

37,135 

37 

143     0 

37 

;150 

0 

37 

157"  6 

Iss 

134      8 

33;  142 

6 

38 

150      S 

38 

|l59 

G 

38jl66      5 

3. 

1142      0 

39;i50 

5 

39 

159      0 

39 

:i67 

9 

39  176     0 

40!l49      5 

!  4o!l58 

0 

i40 

167      G 

4C 

)il76 

0 

4cil85      0 

A  TABLE  OF  ROUjVD  TIMBER, 


15 

22  Ft. 

1  Zi    . 

Long. 

1  o 

3 

1— • 

O 
o 

o 

6 

4   o 

7 

5   9 

1  * 

7   7 

:   9 

9   7 

10 

12   1 

»1 

14  6 

!l2 

17   4 

113 

20   4 

!U 

23   6 

.15 

27  4 

16 

31   0 

17 

o4  9 

18 

39   0 

,19 

i 

43   3 

ho 

48   3 

53   0 

22 

58   1 

23 

63  7 

■:^ 

69  4 

25 

75      S 

26 

81   5 

27 

«7  7 

28 

94   5 

29 

101   0 

30 

lOg   8 

31 

U6   0 

32 

124  0 

33 

!3l   5 

34 

139   4 

35 

'47  7 

36 

156   5 

37 

165   5 
'74  5 

3v 

i4   4 

40 

1 93   5 

5  23  Ft.   5  24  Ft. 


?i25  Ft.  I  5  26  Ft.^ 


A  TABLE  OF  ROUND  TIMBER. 


ic'.-i?  Ft.  :|: 

ft) rs 


6 

5 

7; 

7 

s! 

9 

9 

U 

!0 

14 

I  I 

17 

12 

21 

13 

24 

.51 
161 

'•i 
''I 
20J 
2ii 

22; 
23i 


14j  28 
33 
37 
42 
47 
53 
59 
65 
71 
78 
24;  85 
25;  92 

26  99 

27  107 
|28jiie 

29.124 
3.ri33 
31142 

32  152 

33  IGI 
34;i7l 
35'l8iJ 

36  192 

37  2)6 
3«2U 
39^*26 
40  237 


28  F 

Li  n. 


't.  ?.j29  Fi. 


2| 
4 
9 
^ 

3; 

9' 

9 

5 

9 

6 

b 

5 

2 

0 

5 

5 

3 

5 

7 

7 

0 

2 

2 

3 

i 
8 

5 
( 


7 

8 

y 

10 

i ; 
12 

13 

15 

\v 
17 
18 

20 


7 

9 
12 
15 
!8 
22 
2d 
30 
34 
39 
44 
49 
55 
61 
67 
74 


88 
95 
103 
iil 
I/O 
28 
'36 
147 
157 
167 
178 
188 
199 

.■,:!- n 

3  8  [2  2  2 
3'M234 
4i'  245 


125 
J26 
27' 
!28 

I 
jou 

l3i 
'3^ 
,33 
:34 

36 

"»  • 


■  1  -s 


5  •  6 
5  I  7 

7,1  8 

4|  - 
4-lt- 

6,11 

l:'l2 
8  I3 

7.  I5 

"lo 

17 

Itii 

,lyj 


2 


2] 

,22 

1^3 

26 
27 
28 
29 


^1 

3  1 

3 

32 

0' 

33 

0! 

34 

7! 

0 

3  f) 

0 

37 

1 

38 

/  ! 

Ft 
0 

40 

o 

o 

3 


7 

10 
i2 
15 
19 
23 
26 
31 
36 
40 


57 

63 

69 

76 

83 

9  1 

99 

107 

1  .5 

124 

'33 

=  43 

!52 

63 

173 

184 

194 

i06 

217 

228 

242 

254 


?i  JO  Ft.:  5 


.OxV^. 


o 

o 

D 
«-^ 


7i 
8 
9 
10 
II 
12 
13 
jU 
1  il5 

:\U 

0|  17 


0  ' 

5 

7 

5 

7 

2 

0 

5 

5| 

7 

0 

1 

7 

0 

t' 

C' 

7 
0 
5 
5 
0 
5 


18 
i9 
■  '■iJ 
21 
22 
-  o 
i4 


o 

8 

10 
13 
16 
19 

23 
27 
32 
37 
42 
47 
52 

65 
72 
79 
86 

94 


-5102 
!26  ill 


27 
~^8 

5 ; ; 
31 

32 


■^7 
08 
3 


11^) 

J28 
138 
148 
158 

169 
179 
190 
202 
2  13 
225 
2:- 6 

251 

2)3 


n  Ft. 

Lrrigr. 

o 

o" 

3 


5 
7 
8 

lo 

ii 
1  . 

13 

U 
15 

2>,ll7 

71)18 


1 

01U2 

5123 
2 
7 
2 


2  , 

-7 
28 
2  , 


^1 

32 
33 
34 
|35 
00 
0'37 
1  pb 
(.|i39 
7  -iO 


6 

8 
10 
13 

17 

2') 

24 

28 

.■»  .-> 
00 

33 

43 

48 

54 

61 

67 

75 

82 

89 

)7 

1-6 

ll4 

123 

132 

142 

152 

163 

174 

135 


1 
3 

8 
7 
1 
6 
4 
6 

o 
O 

5 

4 

6 
1 
7 
5 
0 
5 
5 
0 

7 

«» 
o 

7 

0 
4 
0 
0 
4 


1^6  '  G 

208   0 
^18   5 


2  44 

^72 


A  TABLE  OF  ROUjYD  TIMBER. 


to 


3 

32  Ft. 

Long. 

33  Ft. 

Long. 

1 

34  Ft. 

£;' 

re 

"1 

35  Ft. 

Long. 

5 

36  Ft.  1 

Long. 

O 
o 

3 

Lon 

O 
o 

3 

g- 

O 
o 

3 

O 
.  o 

O 
o 

3 

1^ 
6 

3 

B9 

6 

So 

6 

3 

<-r- 

c 

6 

3 
So" 

6 

3 
cn 

6 

3 

6 

5 

6 

7 

6  9 

7   1 

8 

6 

7 

8 

8 

7 

9 

1 

« 

9  4 

7 

9  6 

-  8 

11 

1 

8 

11 

5 

8 

11 

9 

o 
o 

12  3 

o 

12  6 

9 

14 

2 

9 

14 

6 

9 

15 

1 

9 

15  5 

o 

15  9 

.10 

17 

6 

10 

18 

2 

10 

18 

7 

10 

19  3 

10 

19  7 

11 

21 

2 

11 

21 

7 

11 

22 

5 

11 

23  2 

11 

23  7 

12 

25 

4 

12 

26 

1 

12 

26 

7 

12 

27  7 

12 

28  4 

lis 

29 

5 

13 

30 

6 

13 

31 

4 

13 

32  3 

13 

33  3 

14 

34 

3 

14 

35 

4 

14 

36 

5 

14 

37  6 

14 

38  7 

15 

39 

7 

16 

41 

1 

15 

42 

2 

15 

43  3 

15 

44  5 

16 

45 

0| 

IC 

46 

3 

16 

47 

7 

16 

49  2 

16 

50  4 

17 

50 

5 

17 

52 

0 

17 

53 

4 

17 

55  2 

17 

56  6 

18 

56 

5 

18 

58 

5 

18 

60 

1 

18 

62  0 

18 

63  6 

19 

63 

0 

19 

65 

0 

19 

67 

0 

19 

69  0 

19 

70  9 

20 

70 

2 

20 

72 

2 

20 

74 

4 

120 

76  7 

20 

79  0 

21 

76 

7 

21 

79 

5 

21 

81 

7 

21 

84  4 

21 

86  5 

[22 

84 

5 

22 

87 

2 

22 

89 

5 

22 

92  5 

22 

95  4 

'23 

92 

4 

23 

95 

5 

23 

98 

3 

23 

101  2 

23 

104  6 

24 

100 

8 

24 

104 

0 

24 

107 

0 

24 

10  5' 

24 

13  6 

25 

09 

5 

25 

13 

0 

25 

15 

7 

25 

19  5; 

9h 

23  0  \ 

26 

18 

5 

26 

22 

0 

26 

25 

8 

"G 

29  5 

2e 

33  0 

27 

27 

5 

27 

31 

5 

27 

35 

2 

27 

39  5 

2  7 

42  5 

^28 

37 

5 

28 

41 

5 

28 

45 

5 

28 

50  3 

28 

54  4  , 

^0, 

46 

4 

29 

51 

6 

29 

55 

5 

9Q 

61  o! 

29 

65  0 

.30 

57 

0 

30 

62 

6 

30 

67 

0 

36 

72  5J 

30 

77  5 

31 

69 

0 

31 

74 

C 

31 

79 

0 

31 

82  41 

3] 

90  0 

.32 

80 

0 

32 

85 

5 

32 

91 

0 

32 

97  C 

32 

202  0 

.33 

91 

g 

33 

97 

0 

33 

202 

5 

33 

2G8  0 

33 

14  0 

34 

202 

5 

3,4 

208 

2 

34 

14 

3 

34 

20  C 

34 

27  0 

35 

14 

0 

35 

20 

5 

35 

27 

0 

35 

34  0 

35 

40  0 

36 

26 

^ 

36 

33 

5 

36 

40 

0 

36 

47  C 

36 

55  0 

37 

40 

^ 

•37 

47 

r. 

27 

54 

3 

37 

62  5 

37! 

69  5 

38 

53 

5 

38 

61 

5 

38 

68 

0 

3i, 

76  4 

3C 

84  0 

31) 

67 

^^ 

39 

75 

C 

3; 

83 

2 

39 

■^  -'5 

39 

300  0 

iO 

80 

0|i40| 

S8 

5 

40  97 

3 

40 

306  4 

40 

}'     ^  » 

G 

A  TABLE  OF  ROlWD  TIMBER 


72     »||l£'   74     7|iiyj  76     7|jl9j  78     V\19\  80     4 


;  ->-, 


'■>-■•    r  — 

.-oi  o. 


i53    21 

•M;  34 

5:  -n 


31  Oii^c;  83  3;i^0|  S5  bi\20    87  5  120,  89 

88  £ii2l»   91  ^pr-  9d  7i21    96  0  fSl!  98 

07  7i!2e:iOO  5li^:|103  2j[22'l06  OjeellOG 

[07  r   ;^    ^  ■  ■'  '  -      ^^  "  ^^    1-  -'  ::^'  19 

1 .-  .  .  -  :     29 

40 
51 
63 
75 
88 

:02 

14 


t?o 


-r-r 

55 

oii 

92 


5!!:?7^ 


at 

48 

59 

OlUO:  72 

C|i\?9'  82 

o'lSO;  97 

J05     0i:31  211 

IS     0132.  24 


«>;  — 


32  5|i33 

3?  43  01^34 

54     L,    :,  62  0|l3:> 

67     5ii3ii{  76  o!:3a- 


33 
53 
68 
83 


:::i     u.  -l- 


4i 


{33!  43 
x,i34'  58 
obo!  74 
89 
■  •07 
24 
41 
.u,  59 


0 

4 

6 

5 

0 

4 

5 

0 
o 

0 
0 

0 
5 
0 
0 
0 

0 
o 

0 


A  TABLE  OF  ROUXD  TIMBER. 


v^ 

42  Ft. 

^ 

13  Ft. 

C 

i44Ft.| 

w* 

.45  Ft.;  ^46 Ft. 

^' 

Lon 

g- 

2: 
6 

Lon 

or. 
•5' 

3 
0 

-! 
\    =" 

6 

Long,  j 

I 

6 

1  Lons".  1  %"■  Lons:. 

-5 

Q 

1  ' 

0 

0 

0 
0 

CO 

1  ^ 

c 

a 

• 

6 

0 

6 

8 

Q 

8 

4 

3 

i 

8-8 

9  0 

-  7 

11 

3 

7 

11 

5 

7 

11 

7 

12  Oj  7 

12  3 

;  8 

14 

1' 

8 

15 

1 

8 

15 

A 

8 

15  7i  8 

>16   1 

9 

19 

5 

9 

19 

1 

9 

1  19 

4; 

9 

19  8  9 
24  6  10 

20  4 

10 

22 

9 

10 

23 

5 

10 

24 

0; 

10 

25  3 

11 

27 

7 

11 

28 

4 

11 

29 

2; 

11 

29  6  11 

30  5 

12 

33 

o:|i2 

33 

9' 

12 

34 

■^! 

12 

35  4fl2 

36  4 

:  13 

38 

7; 

13 

39 

7 

13 

40 

5! 

13 

41  4!|13 

42  5 

14 

44 

7; 

14 

45 

91 

14 

46 

9| 

14 

48  Ojlu 

49  4 

15 

51 

7 

15 

53 

3!ll5 

52 

■2| 

■  5 

55  5  15 

57  0 

16 

58 

5 

16 

60 

4 

16 

61 

5! 

16 

62  8 

16 

64  6 

17 

66 

0; 

n 

67 

7 

17 

69 

4! 

17 

70  7, 

17 

72  7 

1  18 

74 

2 

18 

76 

0 

18 

'77 

6il8 

79  5i|l8 

81  6 

|19 

82 

5i 

19 

84 

^i 

19 

86 

5l!l9 

88  4!!l9 

90  3 

•20 

91 

^1 

20 

94 

6 

20 

96 

^1 

20 

98  5'|20 

100  5 

1^1 

100 

81 

21 

103 

4 

21 

105 

5'|21 

108  3;!  21 

10  5 

22 

11 

0 

22 

13 

^i 

22 

16 

0| 

22 

18  4:i22 

21   5 

23 

21 

3| 

23 

24 

5! 

23 

27 

31 

23 

29  6II23 

33  0 

•24 

32 

o; 

24 

35 

0 

24 

33 

7J 

24 

41   5i 

24 

"'44  5 

25 

43 

o\ 

25 

47 

3 

25 

60 

^i 

25 

53  7j 

25 

67  0 

26 

53 

o' 

§6 

59 

^■ 

26 

62 

M 

26 

QQ     5] 

26 

70  5 

r' 

67 

0 

27 

71 

0 

27 

75 

0| 

27 

79  Oj 

27 

83  0 

{28 

80 

21 

28 

84 

" 

28 

88 

5! 

28 

93  0 

28( 

97  0 

j29 

92 

8i 

29 

97 

0 

29  201 

^i 

29 

213  0  29 

211  -0 

•30 

206 

^1 

30 

211 

5 

30  15 

0, 

30'' 

21  0;3e 

25  0  , 

31 

20 

i 

31 

25 

2 

31  21 

0i31 

36  0 

31 

42  0 

32 

34 

5 

32 

41 

0 

32 

45  . 

4  32 

52  6 

32 

57  5  ; 

S^ 

49 

0 

33 

56 

1 

3Z>    62 

0,133 

67  5; 

33 

73  0 

34 

64 

0| 

34 

71 

5 

34  76 

5134 

83  5| 

34 

89  0  i 

35 

82 

I 

35 

87 

0 

35  i  94 

0!35 

3Gi  6ii35! 

307  5  i 

36 

96 

0 

m 

304 

oi 

361310 

3136 

17  6;|36 

25  0  1 

37 

314 

5 

37 

22 

1—1 

■37 

28 

0  37 

36  5;|37 

44  0  1 

38 

32 

i: 

38 

37 

5!!38| 

45 

0  38 

55  0;!3Cj 

63  2  ] 

39 

49 

Ci 

39 

57 

1! 

39 

QQ 

4 

39| 

75  0;38| 

84   0  : 

40 

67 

3J140 

.77 

— *■ 

40 

85 

0 

loi 

94  0'40l 

403  1 

X      I 


A  TABLE  OF  ROUXD  TIMBKR. 


o:47  Ft.lf 

'^^  _ 

48  Ft.! 

9. 49  Ft.!  Cj, 

50Ft.il5! 

51  Ft. 

"5 

6i 

Lono;.  1 

o 

1 

a 

1 

o  - 

-5 

6" 

Lonjj;. 

5 

Q 

Lono; 

O 
o 

a 

D 
<-♦■ 

C/3 

II 

3 

(t 

6" 

Long 

I 

5 

Lono;, 

O 
o 

O) 

O 
o 

a 

a 

(A 

o 
3d 
6 

o 

o 

D 

• 

9  2] 

9  41 

6 

9 

6 

9 

8 

9  9 

7 

12  6i 

7 

12  8  7 

13 

1 

7 

13 

4 

7 

13  7 

8 

16  4 

I 

16  7  8 

17 

1^ 

8 

17 

5 

8 

17  8 

9 

20  7! 

9 

21   1|  9  21 
26  3:  10  26 

6 

9 

22 

0 

e 

22  5 

10 

25  7 

10 

10 

27 

S 

10 

27  8 

^i; 

31  0,11 

31   7  11 

32 

3 

11 

32 

9|11 

33  7 

12| 

37  0 

12 

37  7  12 

38 

6| 

12 

39 

3112 

40  1 

13| 

43  SJ 

13 

44  0  13 

45 

o! 

13 

45 

9  13 

46     9 

!  14 

50  41 

14 

51  2 

14 

52 

3, 

14 

53 

2;14 

54  6 

'■   15 

58  0. 

15 

59   1 

15 

60 

S| 

15 

61 

7  15 

63  2 

i  13 

65  G, 

16 

67  0 

16 

68 

^1 

16 

70 

0|16 

71  6 

i  1"^ 

73  8i 

17 

75  Si!l7 

77 

i 

17 

78 

8 

in 

80  4 

i  18 

83  3| 

18 

84  5:118 

86 

4 

18 

88 

0 

:18 

90  3 

:i9 

92"  4| 

19 

94  S;!19 

96 

3' 

19 

98 

3 

'19 

100  7 

i  20 

102  5' 

2G 

105  0i:20|l07 

0 

20 

109 

3 

'20 

12  0 

121 

13  0| 

21 

15  3|21 

17 

4 

21 

20 

0 

21 

21   5 

[22 

23  5| 

22 

26  7|;22 

29 

0 

22 

32 

0 

22 

35  0 

f  23 

35  5| 

23 

38  5 

23 

41 

5 

23 

44 

0 

33 

47  6 

24 

47^0' 

24 

50  8 

24 

53 

5| 

24 

57 

0 

'24 

60  7 

25 

60  5 

23 

63  6j|25 

67 

0 

25 

71 

0 

25 

72  6 

126 

73  2 

26 

77  5|  26 

81 

26 

83 

2 

26 

89  0 

i27 

87  O' 

27 

91  0:27 

95 

0 

27 

98 

4 

,27 

202  6 

1^28 

;201   5 

28 

205  0j28 

209 

0 

68 

214 

0 

i28 

17  5 

29 

1-14  0 

29 

18  0:29 

24 

0 

29 

28 

0 

29 

33  5 

i  30 

30  0 

30 

35  7|30 

40 

3 

30 

45 

0 

'30 

50  0 

Isi 

45  5 

31 

52  031 

57 

0 

31 

62 

5 

31 

67  6 

.  32 

62  5!i32 

67  21 32 

74 

0 

32 

78 

5 

l32 

85  0 

t33 

78  0 

33 

85  0 

i3.'3 

91 

5 

33 

96 

5 

33 

303  6 

(34 

95  0 

,34 

302  5 

34 

308 

0 

34 

315 

0 

j24 

21   5 

i3£ 

313  4 

:3s 

20  0 

|3£ 

27 

2 

35 

33 

5 

|35 

40  0 

!3C 

32   1 

136 

38  0 

,36 

4b 

0 

36 

53 

C 

36 

61  0 

I  31 

,  52  ( 

\3', 

59  1 

1  -^^ 

'  G6 

3 

37 

74 

c 

|37 

82  6 

i3£ 

I    70  0 

.SI 

78  7 

38!  86 

5 

'38 

94 

€ 

3£ 

403  0 

i3e 

->    90  C 

l3G 

^98  5'  39  407 

5 

'39 

416 

C 

3£ 

23  5 

!4( 

)411   2''4( 

H18  5|40  27 

6 

4C 

36 

t 

4C 

»  46  0 

^ 


A  TABLE  OF  ROUXD  TIMBER^ 


t  i 


^— ' 

52  Ft.| 

s-^ 

53  Ft. 

jc 

54Ft.| 

'w 

i)^  Ft. 

I  ^ 

56  Ft. 

1 
(T 

Lons:.  i 

0 
0 

a 

3 

"1 

Lon 

?. 

:  ^ 
If 

Lon 

Z-   ' 

5 

-5 

Lon 

rr. 

^ 

11 

1  -1 

Lon 

0 
0 

3 

V, 

0 
0 

0 
0 

0 
0 

3 
V. 

-6 

1 
1 

1 

6 

|5" 

6 

3 

!-- 
i  6 

3 

10 

2 

10 

~4 

10 

"6 

10 

8 

11 

~0 

7 

13 

9; 

7 

14 

1 

■7 

14 

4: 

14 

7 

;  -7 

14 

9 

C 

18 

2 

8 

18 

5 

8 

18 

s; 

8 

19 

3 

is 

19 

5 

c 

22 

8, 

9 

23 

3 

9 

23 

7 

9 

24 

0 

;  0 

24 

7 

10 

28 

4; 

10 

28 

8 

10 

29 

4| 

10 

30 

0 

10 

50 

7 

U 

34 

0' 
0, 

11 

34 

9 

In 

35 

5 

11 

36 

^ 

11 

36 

8 

12 

40 

9 

12 

41 

0 

12 

42 

i 

12 

43 

3 

12 

44 

0 

13 

47 

8' 

13 

48 

7 

13 

49 

1\ 

13 

50 

1 

|13 

51 

5 

U 

55 

6' 

14 

56 

0 

14 

57 

7: 

14 

53 

8 

Il4 

59 

8 

15 

64 

3 

15 

65 

4 

15 

m 

6 

15 

67 

2 

15 

69 

3 

16 

72 

7! 

16 

74 

0 

:i6 

75 

4 

16 

77 

0 

!16 

78 

5 

17 

82 

0 

n 

83 

0 

:i7 

84 

8: 

17 

86 

6 

In 

88 

0 

18 

92 

0 

18 

93 

5 

18 

95 

5' 

18 

96 

4| 

|18 

98 

7 

19 

101 

3. 

19 

104 

0 

19 

106 

5 

19 

103 

< 

119 

UO 

7 

20 

14 

0 

20 

15 

5 

20 

17 

9- 

20 

20 

5 

|2C 

22 

5 

21 

25 

0 

21 

27 

0 

21 

29 

Oi 

21 

32 

^i 

121 

34 

4 

22 

37 

^'. 

22 

39 

5 

22 

42 

3 

22 

45 

3! 

I22 

48 

0 

-23 

50 

5 

23 

53 

0 

;23 

55 

3, 

23 

59 

oi 

23 

60 

0 

2-1 

61 

5 

24 

QQ 

5 

24 

69 

5 

24 

73 

ol 

24 

77 

0 

25 

78 

Oi 

26 

81 

0 

''25 

84 

5 

25 

88 

0 

25 

91 

5 

26 

92 

8! 

26 

95 

5 

:26 

98 

26 

203 

0 

26 

207 

0 

27 

214 

0' 

27 

209 

0 

,27 

217 

oi 

27 

17 

o;27 

32 

0 

^0 
^0 

23 

0 

28 

26 

0 

128 

32 

^i 

28 

35 

5I20 

38. 

0 

29 

37 

5' 

29 

42 

0 

29 

47 

0' 

29 

52 

0129 

56 

0 

30 

55 

0 

30 

60 

0 

30 

65 

0; 

30 

70 

G 

30 

75 

0 

31 

73 

0' 

31 

77 

5 

31 

83 

4,31 

88 

0 

31 

9' 

32 

91 

0 

32 

95 

0,32 

303 

0'32 

307 

6 

32 

31.3 

li 

33 

310 

0 

33 

315 

0j33 

22 

0 

33 

26 

5 

33 

34 

0 

_, 

34 

29 

0, 

34 

33 

0  34 

41 

^i 

34 

46 

0 

34 

54 

5 

35 

47 

5 

35 

54 

5  35 

62 

0^ 

35 

67 

0 

3lD 

75 

0 

67 

0 

36 

74 

8  j3G 

83 

0 

0  ■^ 

'jO 

89 

V' 

m 

96 

5 

37 

90 

0 

37 

97 

0  37 

405 

0,137 

413 

r 
0 

l3; 

+  10 

0. 

.0 

411 

0 

38 

416 

5  38 

26 

4;  3d 

33 

0 

38 

41 

5 

19 

32 

0 

39 

40 

0,;39 

49 

5i  39 

53 

0 

39 

66- 

3 

40 

54 

0 

40 

63 

5  '40 

72 

0'140 

81 

5 

140 

■  S9^ 

6 

02 


A  TABLE  OF  ROUND  TIMBER. 


>^ 

57  F 

't.;!? 

581^ 

't.i 

:  ^ 

59  Ft.] 

:? 

60  F 

't.i 

o 

61  Ft.  1 

3 
1 

■  -5 

Long. 

;  2. 

Loni 

T 

a. 

Lons;. 

B 

Lons 

T 

O 
o 

o 

O 
o 

o 

o 

D 

o 

o 

3 

t/. 

c 

2 

:  ^ 

: 

1  G 

o 

en" 

or. 

1 

6 

1 

6 

3 

<X1 

V. 

6 

cn 

D 
•-♦• 

12 

'~0 

11 

i^' 

'\\~ 

4 

11 

5 

11 

"8' 

1 

15 

c 

•7 

15 

o 

7 

15 

8 

7 

16 

0 

7 

16 

3 

r 

19 

( 

8 

20 

5 

1  ^' 

20 

6 

8 

20 

9 

C 

21 

3 

q 

25 

I 

9 

25 

7 

i  9 

26 

0 

9 

26 

< 

9 

26 

8 

10 

31 

o 

10 

31 

7 

10 

32 

3 

10 

32 

1 

7; 

10 

33 

4 

11 

37 

c 

111 

38 

'^ 

11 

38 

8| 

11 

39 

6- 

11 

40 

o 

12 

44 

Il2 

45 

7 

'12 

46 

5 

12 

47 

4i 

12 

48 

0 

13 

52 

4 

!l3 

1 

53 

5 

13 

54 

4! 

13 

65 

I 

4! 

13 

56 

3 

14 

60 

^ 

|14 

62 

0 

14 

63 

^i 

14 

64 

2;ii4 

65 

3 

15 

70 

5 

il5 

72 

2 

|15 

73 

2 

15 

74 

3^ 

15 

75 

7 

16 

79 

< 

16 

81 

5 

!l6 

82 

7 

16 

84 

4" 

16 

85 

5 

17 

89 

r 

'n 

91 

5 

h' 

92 

8 

17 

94 

5^ 

17 

96 

2 

18 

101 

c 

jl8 

103 

0 

il8 

104 

8 

18 

106 

5| 

18 

108 

5 

19 

12  • 

Cil9 

14 

^ 

;19 

16 

o 

19 

18 

o;|i9 

20 

3 

2U 
21 

25 
37 

C 

3 

'20 

121 

27 
39 

ol 

120 
121 

29 

42 

0 

0 

20 
21 

31 

42 

^i'i*^0 

6121 

33 
46 

5 
5 

22 

50 

4 

|22 

43 

0| 

;;22 

55 

122 

58 

5122 

61 

4 

23 

64 

^-• 

123 

68 

0 

23 

71 

0 

23 

73 

523 

77 

0 

2-1 

79 

r 

124 

c 

|24 

86 

0 

24 

89 

^ 

24 

92 

8 

21 

85 

Oi25 

98 

2 

i25 

202 

5 

25 

205 

o' 

25 

207 

0 

26 

210 

( 

i26 

213 

5 

'26 

17 

6 

26 

21 

5' 

26 

25 

0 

27 

25 

K.' 

:27 

30 

0 

i27 

34 

^^i 

27 

38 

0: 

27 

42 

0 

Oo 

43 

/;. 

j28 

47 

5 

|28 

52 

5; 

28 

57 

o| 

28 

62 

2 

29 

62 

^ : 

29 

65 

0 

!2C 

70 

0 

29 

74 

^1 

29 

79 

0 

30 

81 

r  i30 

85 

2' 

30 

87 

5 

30 

94 

0: 

30 

300 

0 

31 

300 

Gpl 

305 

0 

'31 

309 

^ 

31 

315 

o| 

31 

21 

0 

32 

20 

2|!32 

25 

c 

|32 

30 

^ 

32 

35 

0i32 

42 

5 

33 

40 

0 

33 

45 

6 

j33 

52 

c! 

33 

56 

5i33 

64 

0 

34 

61 

6 

34 

65 

5 

|34 

73 

^i 

34 

78 

0!|34 

85 

0 

3:. 

82 

.35 

87 

C 

,35 

95 

0 

35 

402 

s' 

35 

408 

0 

3C 

105 

0 

36 

409 

c 

'36 

416 

3 

36 

24 

0 

36 

31 

5 

3»^ 

27 

V 

o 

37 

33 

o 

<.-•■ 

;37 

42 

0 

37 

48 

0 

57 

56 

5 

3r 

51 

c 

|38 

5G 

C-! 

38 

65 

0 

38 

74 

0 

38 

82 

0 

1.. 

Ob 

75 

c 

39 

82 

t: 

39 

91 

^) 

39 
4(1 

98 

5j39 
4)40 

507 

2 

4(; 

\   98 

5 

10 

50Q 

5 

'40 

516 

cj 

524 

33 

.\ 

A  TABLE  OF  ROiWD  TIMBER. 


g 

62  Ft. 

c 

63  Ft. 

1  D 

64  Ft. 

C 

651^ 

t. 

1  ~ 

66  Ft.  1 

cr. 

6 

Lot), 

y^ 

3 

5" 
6 

Lon 

0-.    \ 

-i' 

B 
re 

i" 

6 

Lon 

f**. 
■> 

I 

i  5 

1  -  • 

CO 

6 

Lotjo;. 

5 
2- 

►—1 

X 

6 

Lon* 

o 

E. 

r. 

O 
o 

O 
o 

n 

»-♦■ 

O 

o 

O 

a 

CA 

o 

o 

s 

t-t- 

s 

12 

2 

12 

4 

12 

6 

12 

8 

13 

"o 

7 

16 

6 

7 

16 

9 

7 

17 

Q 

7 

17 

4 

7 

17 

7 

8 

21 

6 

8 

22 

0 

8 

22 

4 

8 

22 

7 

8 

23 

1 

9 

27 

3 

9 

27 

7 

9 

28 

2 

9 

28 

7 

9 

29 

2 

10 

33 

8 

!io 

34 

6 

10 

35 

2 

10 

35 

6 

10 

36 

2 

11 

40 

8 

111 

41 

6 

11 

42 

3 

11 

42 

9 

11 

43 

6 

12 

48 

7 

12 

49 

6 

12 

60 

4 

12 

51 

3 

12 

52 

0 

13 

67 

2 

13 

68 

2 

13 

69 

0 

13 

69 

8 

13 

60 

8 

14 

Q6 

o 

14 

67 

4 

14 

68 

6 

|14 

69 

7 

14 

70 

6 

15 

76 

7 

15 

77 

0 

15 

78 

4 

jl5 

80 

9 

15 

82 

2 

16 

86 

8 

16 

88 

3 

16 

89 

6 

jie 

91 

5 

16 

92 

5 

17 

97 

6 

17 

99 

0 

17 

100 

8 

17 

103 

G 

il' 

104 

5 

IG 

109 

6 

18 

112 

0 

18 

13 

6 

\\% 

15 

0 

18 

17 

0 

19 

22 

0 

il9 

24 

4 

19 

26 

2 

19 

28 

6 

19 

30 

7 

20 

36 

0 

,20 

38 

0 

20 

40 

7 

i2C 

42 

8 

20 

45 

0 

21 

48 

8 

21 

61 

5 

21 

64 

2 

21 

56 

5 

21 

59 

0 

22 

63 

5 

22 

65 

0 

22 

69 

5 

22 

72 

5 

22 

75 

0 

!23 

79 

0 

83 

0 

23 

85 

o 

!23 

89 

0 

23 

91 

3 

24 

96 

0 

24 

98 

0 

24 

202 

0 

24 

205 

0 

24 

207 

5 

15 

211 

5 

|26 

214 

5 

24 

13 

0 

|25 

22 

2 

25 

25 

5 

:;6 

28 

0 

26 

32 

6 

20 

26 

0 

26 

40 

0 

26 

43 

2 

■27 

46 

0 

27 

^\ 

0 

27 

54 

2 

127 

58 

0 

27 

62 

5 

*28 

65 

0 

28 

70 

0 

28 

73 

6 

128 

77 

2 

28 

92 

5 

29 

83 

5 

2P 

88 

c 

29 

93 

^2c 

97 

6 

29 

303 

0 

50 

305 

2 

30 

309 

5 

'30 

315 

C 

30 

319 

6 

30 

24 

5 

31 

25 

5 

31 

32  • 

0 

131 

35 

6 

31 

42 

0 

31 

46 

5 

32 

46 

0 

32 

53 

c 

!32 

58 

6 

:32 

64 

5 

i32 

70 

5 

33 

68 

0 

33 

75 

c 

'33 

83 

0 

'33 

87 

6 

|33 

94 

0 

34 

90 

0 

34 

97 

Q 

34 

404 

7 

i34 

4n 

5 

!34 

416 

6 

35 

414 

c 

135 

421 

5 

36 

26 

i36 

34 

0 

35 

42 

0 

36 

37 

3 

36 

45 

c 

36 

53 

2 

36 

59 

0 

3t; 

67 

0 

37 

64 

C 

'37 

71 

5 

•37 

80 

0 

:37 

87 

6 

137 

95 

0 

38 

88 

c 

38 

96 

6 

138 

504 

5 

38 

513 

5 

•38 

511 

% 

39 

515 

p. 

3£ 

523 

r. 

.39 

32 

t-. 

3f- 

41 

3 

48 

6 

40 

41 

4 

40 

61 

oi 

40 

57 

4(: 

67 

0'40 

76 

5 

80 


A  TABLE  OF  ROUXD  TIMBER. 


3 

67  Ft. 

C 

68  Ft. 

•^^ 

69  Ft. 

■w 

70  Ft. 

>-' 

71  Ft. 

6 

Lons;. 

§ 

rt- 

CD 

<^ 

G 

Long. 

§ 

o 

■J. 

C 

Long. 

6' 

Long,  j 

ft 

D 

6 

Lone:. 

o 

.  o 
a 

o 

3 
tn 

O 
o 

s 

r-f- 

o 

3 

Cft" 

O 
o 

3 

a> 

3 

r-r- 

13  4 

O 
o 

D 

ft) 

=5 

13  G 

O 
o 

Q 

1 

13  2 

13 

13  9 

7 

18  0 

7 

18  2 

19  6 

7 

18 

19  0 

8 

23  4 

o 
O 

23  6 

8 

24  2 

8 

24 

4 

8 

24  7 

9 

29  6 

9 

29  7 

9 

30  3 

9 

30 

7 

9 

31   3 

10 

36  6 

10 

37  2 

10 

37  6 

10 

38 

2 

10 

38  8 

11 

44  2 

11 

44  7 

11 

45  6 

11 

46 

1 

11 

46  7 

12 

62  6 

12 

53  4 

12 

54  S 

12 

54 

o 

12 

66  8 

13 

61   5 

13 

62  5 

13 

63  6 

13 

64 

3 

13 

65  0 

14 

71   7 

14 

72  5 

14 

73  6 

14 

74 

6 

14 

75  8 

15 

83  4 

16 

84  3 

16 

85  6 

16 

66 

6 

16 

87  8 

16 

94  0 

16 

95  3 

16 

96  6 

16 

97 

8 

le 

99  2 

17 

1C6  0 

17 

107  2 

17 

109  0 

17 

110 

s! 

17 

114  0 

18 

18  6 

18 

12  6 

18 

22  6 

18 

23 

5 

18 

25  5 

19 

32  5 

19 

34  0 

19 

36  6 

19 

38 

0 

19 

40  0 

20 

40  8 

20 

48  6 

20 

51   5 

20 

53 

0 

20 

55  2 

21 

61   2 

21 

63  2 

21 

61   6 

21 

68 

0 

21 

71   0 

oo 

78  0 

22 

80  6 

22 

83  0 

22 

85 

0 

oo 

88  0 

23 

94  0 

23 

96  0 

23 

99  0 

-0<2 

204 

0 

23 

205  0 

24 

211   6 

24 

213^  0 

24 

216  5 

24 

18 

c 

^4 

22  5 

26 

28  0 

26 

32  0 

op. 

35  6 

ox 

37 

c 

26 

42  0 

2G 

47  0 

26 

51   5 

26 

55  0 

26 

57 

r 

26 

62  2 

-27 

66  5 

27 

69  0 

27 

74  C 

27 

76 

(• 

1^7 

81   5 

28 

86  6 

28 

90  0 

28 

94  6 

28 

97 

r 

]28 

303  6 

29 

306  6 

29 

311   0 

29 

315  6 

29 

318 

t^ 

129 

25  0 

.;o 

28  0 

30 

33  0 

30 

37  0 

30 

43 

( 

30 

48  2 

31 

62  0 

31 

66  0 

SI 

62  0 

31 

66 

( 

31 

73  0 

32 

75  4 

32 

81  6 

32 

87  2 

32 

91 

( 

t'32 

97  0 

^;3 

93  6 

33 

404  5 

33 

411   6 

33 

415 

r 

!33 

422  5 

31 

422  6 

34 

27  0 

34 

34  6 

34 

39 

( 

:34 

46  6 

36 

47  0 

36 

63  6 

36 

61  0 

36 

66 

(. 

36 

".2     0 

3G 

74  0 

36 

79  0 

36 

88  0 

36 

94 

(' 

36 

501  5 

37 

602  0 

37 

507  '  0 

37 

515  6 

37 

503 

i* 

37 

30  0 

,i8 

27  0 

38 

34  0 

3F: 

43  6 

38 

50 

c 

,38 

57  0 

39 

65  6 

39 

63  0 

3C 

73  6 

39 

80 

c 

139 

88  5 

+0 

84  0 

40 

92  2 

40 

0(^3   - 

■\( 

6v> 

( 

'40'61B  5  1 

A  TABLE  OF  ROUXD  TIMBER. 


81 


ffFt 

^ 

73  Ft. 

$74.  Ft 

1  5  75  Ft. 

CT 

76  Ft. 

Lon 

§• 

K 

3 
ft 

3 
Cfi 

6 

Lona:. 

1 

re 

<-► 

3 
m 

6 

Lon 

K- 

i 

o 
o 

3 

Ml 

6 

Lon 

(T 

2. 
6 

Lon^. 

O 
o 

a 

o 

o 

o 

D 
«-* 

O 
o 

3 

2. 

00 

O 
o 

3^ 

1 

0 
0 

3 
«-»■ 

3 

14 

1 

14 

3 

-IT 

6 

i  14 

'/ 

14  9 

7 

19 

2 

7 

19 

5 

7 

19 

8 

7 

20 

0 

7 

20  4 

8 

25 

2 

8 

25 

5 

8 

25 

8 

8 

36 

8 

26  6 

0 

31 

7 

9 

32 

2 

9 

32 

7 

9 

73 

1 

9 

33  6 

10 

39 

o 

10 

39 

10 

40 

5 

10 

41 

0 

10 

41   7 

n 

47 

5 

11 

47 

3 

11 

48 

9 

11 

49 

4 

11 

50  4 

12 

56 

6 

12 

57 

5 

12 

58 

3 

12 

58 

9 

12 

60  0 

13 

65 

2 

13 

68 

0 

13 

67 

6 

13 

69 

0 

13 

70  4 

14 

76 

7 

14 

78 

0 

14 

79 

4 

!14 

80 

3 

14 

81   5 

15 

88 

8 

15 

91 

0 

15-  92 

0 

15  93 

0 

15 

94  5 

16 

100 

7 

16 

102 

5 

16 

104 

5 

16  105 

0 

16 

107  0 

17 

13 

6 

17 

15 

0 

17 

17 

0 

jl7  18 

0 

i; 

20  5 

18 

27 

5 

u. 

29 

0 

18 

31 

5 

!l8 

32 

5 

18 

35  0 

1? 

41 

5 

19 

44 

0 

19 

46 

5 

!19 

47 

5 

19 

50  7 

20 

57 

0 

20 

61 

0 

20 

62 

5 

(20 

64 

0 

JO 

67  0 

tl 

73 

0 

21 

76 

0 

21 

78 

5 

!21 

81 

0 

21 

e3  5 

22 

91 

0 

22 

93 

0 

22 

96 

0 

22 

97 

6 

22 

200  5 

23 

207 

0 

23 

211 

0 

23 

204 

0 

23 

216 

5 

33 

18  0 

24 

26 

0 

24 

28 

0 

24 

32 

5 

24 

35 

0 

24 

38  0 

25 

46 

0 

i5 

48 

0 

25 

52 

6 

!25 

56 

0 

25  59   0  1 

26 

65 

6 

26 

69 

0 

26 

73 

5 

126 

77 

0 

26 

81   5 

27 

85 

0 

27 

88 

2 

27 

93 

5 

127 

98 

5 

27 

303  2 

28 

307 

2 

28 

312 

5 

28 

316 

5 

-8 

310 

0 

28 

25  5 

29 

28 

0 

29 

34 

0 

29, 

38 

0 

29 

43 

0 

29 

47  3 

30 

53 

0 

30 

58 

0 

3o' 

62 

5 

30 

67 

5 

30 

74  0 

31 

77 

0 

31 

84 

0 

31  89 

0 

31 

94 

0 

31 

99   0 

32 

403 

5 

32 

409 

0 

32 

415 

0 

32 

419 

0 

32  425  3  1 

33 

26 

5 

33 

34 

0 

33 

40 

0 

33 

45 

0 

33, 

53   5 

34 

53 

0 

34 

59 

0 

34 

66 

0 

34 

73 

5 

341 

79   0 

35 

81 

0 

35 

88 

0 

35 

95 

0 

35 

501 

0 

35' 

508  0 

36 

507 

2 

36 

514 

5 

36 

522 

5 

36 

27 

5 

36  i 

36  5 

37 

37 

0 

37 

45 

0 

37 

53 

0 

37 

59 

0 

37 

67  0 

38 

65 

0 

38 

73 

0 

38 

82 

0 

38 

88 

0 

38 

97  5 

39 

.97 

0 

39 

607 

2 

39 

615 

0 

39 

624 

0 

39 

333  2 

40 

627 

0 

40 

36 

2 

40 

45 

6 

40 

54 

5 

401 

64  2 

82 


J  TABLE  OF  ROUXD  TIMBER. 


<^ 

77  Ft. 

'  o 

78  Ft. 

CT 

79  Ft.! 

w 

80  Ft. 

^i 

8rFt. 

2i 

3 
p 

6 

Long 

O 
o 

D 
a> 

<— - 

^ 

i 

"3 

6 

Long. 

1 
6 

Lons 

o 

o 

"5 

5 
2 

X 

6 

Long. 

0 
0 

r-r- 

1 

3 
6 

Long. 

0 
0 

3 

3^ 

O 

o 

<->■ 
O 

T5~ 

T 

15 

15 

"15   7| 

15   8 

7 

.20 

6 

7 

20 

8 

7 

21 

2 

7 

21   3i 

7 

21   6 

8 

26 

8 

8 

27 

O 

8 

27 

5 

1 

8 

27  7 

8 

28   2 

9 

9 

5 

34 

4 

9 

34 

8 

9 

55   2! 

9 

55   5 

10 

41 

9 

10 

42 

5 

10 

45 

5 

10 

43   6 

10 

44   0 

11 

50 

7 

11 

51 

4 

11 

52 

1 

11 

52   6 

n 

55   5 

12 

60 

4 

12 

61 

12 

62 

2 

l2 

62   6i 

19 

65   5 

15 

70 

8 

13' 

71 

7 

.  5 

72 

5 

13; 

73  4 

15 

74   3 

14. 

82 

5 

14 

83 

5 

14 

84 

5 

14; 

85   2 

14 

86   3 

15 

95 

5 

15 

96 

5 

15 

96 

7 

is! 

98   8 

15'  99   8  1 

16 

108 

5 

16 

109 

o 

O 

16 

no 

8 

16| 

112  0 

|16 

113   0 

\7 

21 

5 

17 

23 

0 

17 

24 

5 

17 

26  51 

1 

!'^ 

27   5 

18 

36 

7 

18 

38 

5 

18 

59 

5 

18 

41   5 

18 

45   0 

19 

51 

5 

19 

53 

5 

19 

54 

4 

19l 

57  0| 

19 

59   0 

20 

66 

0 

20 

71 

0 

20 

73 

0 

20 

1 

75   01 20 

77   0 

21 

85 

2 

21 

88 

0 

21 

90 

5 

2i; 

92   5  21 

94   5 

22 

205 

0 

22 

206 

2 

22 

208 

0 

22' 

210   C  122 

212   5 

23 

22 

2 

23 

24 

5 

25 

27 

0 

25  29   l|25 

52   5 

24 

42 

0 

24 

44 

0 

24 

47 

5 

24,  5  1   5  124 

53   5 

25 

63 

0 

25 

66 

c: 

25 

69 

0 

25 

72   5 

26 

75   0 

26 

84 

0 

26 

87 

0 

26 

91 

0 

26 

94  0 

26 

95   5 

27 

505 

5 

27 

309 

0 

27 

314 

0 

27 

316   3 

27 

321  0 

28 

28 

0 

28 

33 

5 

2  8 

56 

0 

28 

41   C 

28 

45   0 

29 

53 

5 

29 

56 

0 

29 

62 

5 

2y 

65   0 

29 

68   0 

30 

77 

5 

30 

83 

6 

50 

87 

0 

50 

92   5 

50 

96   5 

31 

404 

0 

31 

408 

5 

31 

414 

0 

51 

4I7   3 

51 

422   5 

32 

30 

0 

32 

35 

0 

32 

42 

0 

52 

45   3 

32 

52   0 

33 

58 

0 

33 

64 

2 

53 

68 

c 

.-1  n 
00 

75   0 

00 

79   0 

34 

85 

1 

34 

,  92 

C 

34 

96 

5 

34 

503  0 

54 

507   5 

35 

514 

5 

35 

i520 

0 

35 

526 

5 

35 

33   5 

35 

36   5 

36 

43 

5 

36 

:  50 

0 

36 

56 

e 

36 

62   5 

36 

66   5 

37 

74 

0 

37 

!  85 

0 

37 

89 

2 

37 

96  0 

37 

604  2 

jB'oee 

0 

58 

614 

2 

38 

622 

5 

38 

628   0 

58 

34  5 

39  40 

0 

39 

1  '^« 

39 

57 

2 

39 

65   5 

59 

69  -5 

iO  73 

1 

40 

'  82 

5 

|40 

89 

5 

40 

97   7 

40 

704   5 

A  TABLE  OF  ROUXD  TIMBER. 


83 


c 

182  Ft. 

:  C? 

83  Ft, 

c 

84  Ft. 

?:85Ft. 

u 

86  It. 

3 

CO 

Lono-, 

3 

ft 

Lon 

0 
0 

3 

U- 

1 

Lotl! 

£^l 

il 
-J 

LuMiic- 

:  ^  1 

Long. 

0 

0         1 

3 

0 
0 

3^ 

0 

0 

0 

C 

3 

6 

a 

in 

6 

rJ 

«-»■ 

en 

i 
1 

6 

en 

6 

3 

an 

1    ^^ 

6 

3 

1  6 

1 

16 

16 

~5 

i  6 

7 

16      9 

21 

8 

7 

22 

2' 

7 

22 

4 

7 

22 

7 

7 

22      9    ' 

8 

28 

5 

8 

2  8 

si 

8 

29 

0 

8 

29 

5 

« 

S9      8    ! 

o 

36 

Q 

9 

36 

5 

9 

36 

7 

9 

37 

4 

1  s 

37      S 

IC 

44 

6 

10 

45 

0 
0 

IC 

45 

6 

10 

46 

4 

10 

46      9    i 

1  1 

!  54 

0 ' 
0 

I  i 

54 

6 

11 

55 

2 

I  I 

5  5 

9 

1  i 

56      5 

i2 

64 

4; 

12 

65 

0 

12 

65 

8 

13 

66 

6 

12 

67      6 

13 

75 

5i 

13 

76 

0 

0 

h5 

77 

(■ 

13 

78 

3 

13 

79      3 

U 

87 

51 

14 

88 

5 

iu 

89 

4 

14 

'  91 

0 

14 

92      3 

15 

101 

5 

15 

102 

8 

115 

103 

8 

!5 

105 

6 

.5h06      9 

16 

14 

^i 

16 

16 

2 

|ie 

17 

C 

!6 

18 

8 

16 

20      6 

17 

29 

0' 

17 

31 

0 

■  '7 

32 

0 

17 

34 

-o 

:'7 

36     0 

!S 

46 

oi 

18 

47 

0 

ilS 

48 

2 

'8 

50 

5 

.18 

52      5 

19 

61 

0 

19 

63 

0 

19 

64 

5 

i9 

67 

I 

I  '• 

69      0 

■20 

79 

5' 

20 

82 

5 

20 

83 

0 

20 

86 

5 

•20 

89      0 

21 

97 

0; 

21 

99 

0 

21 

202 

e 

~  i 

204 

0 

21 

206      7 

22 

216 

0; 

22 

218 

0 

22 

20 

0 

22 

23 

5 

,22 

27      0 

25 

36 

5 

23 

38 

5 

2  3 

41 

5 

23 

44 

5 

■  ^  ^> 

48      0 

24 

56 

5 

24 

60 

Ol 

24 

62 

5 

■■>  -I 

o7 

0 

!..4 

70      0 

25 

78 

5 

25 

83 

0 

!25 

85 

o| 

25 

88 

5 

|2;i 

93      5, 

26 

i 

302 

5; 

26 

306 

0 

26 

307 

5: 

26'314. 

0 

2. 

315      0 

271 

35 

0 

27 

28 

0 

I27 

31 

5; 

J? 

36 

5 

'^7 

41       0 

■281 

1 

49 

(• 

28 

55 

5l 

28 

57 

Oi 

28 

64 

0 

-  8 

67      0    , 

29i 

1 

75 

0 

29 

78 

51 

29 

83 

2 

29 

87 

5 

'2  9 

94      0 

.30! 

403 

0 

30 

406 

5\ 

30 

410 

5 

.i(/ 

416 

5 

20 

422       1 

3:1 
1 

28 

Z] 

31! 

34 

si 

^  1 

47 

5 

3! 

45 

C 

,, 

50      0 

32' 

1 

57 

0 

32 

64 

0 

52 

66 

^i 

10^ 

75 

c 

32 

82      0 

331 

86 

( 

00 

94 

0 

33 

96 

5! 

I33 

5C5 

0 

■■•  0 

.}0 

505      5 

34' 

i 

5  15 

2 

34 

5^:, 

2 

134 

525 

o; 

|34 

34 

2 

n 

42      5  , 

35i 

45 

0 

35 

53 

5 

i35 

55 

5; 

35 

65 

( 

j  35 

73      5 

36j    76 

ol 

36 

1 

84 

0 

loo 

89 

Oi 

36 

99 

2 

|36 

607      0 

371613 

''i 

37! 

621 

^> 

i   .1  r 

1 

625 

0! 

38 

636 

0 

37 

44      5 

381    44 

5! 

38 

53 

5i 

lor. 

Ob 

57 

5! 

38 

68 

0 

38 

77      2    1 

JSJ   82 

5 

39 

89 

0 

39 

95 

0! 

39 

706 

( 

39 

r\$    0  ; 

40! 

714 

5 : 

40 

724 

0 

40 

731 

5' 

40 

43 

ij 

-it' 

5-2    5  '■ 

S4 


A  TABLE  OF  ROUJ^D  TIMBER. 


fbl  Ft.i 

C 

88  Ft. 

■  0 

89 1 

't. 

— 

90  t  t.'i  ^ 

91  t\. 

3  Lnos 

r_ 

.<5 

e 

LoriK.  1 

5 
6 

Long. 

0 
5- 

'^  1 

s   1 

So" 

5- 
J'  1 

6 

Long. 

9 

3 

3 

U3 

5 
ft 

<-► 
a 
n 

5" 
6 

Lon?. 

0 
0 

3 

es 

3 

CA 

n 

P", 

6 

O 

o 

3 

0 
0 

CN 

17 

~T 

17 

0 ; 

17 

5! 

17 

1 

17   9 

7 

2S 

2! 

7 

23 

4i 

7 

23 

7 

7 

24 

'! 

7 

24   3 

8 

50 

4! 

8 

30 

7: 

8 

31 

2 

8 

31 

5 

b 

31   7 

^ 

38 

3^ 

9 

38 

7' 

i  9 

39 

3; 

9 

39 

^t 

9 

39   9 

:'c 

47 

5' 

10 

48 

Oi 

10 

48 

71 

lo 

49 

3! 

10 

49   6 

11 

57 

51 

1  1 

58 

1 
0 

11 

58 

6i 

11 

59 

^-' 

11 

59   8 

12 

68 

4; 

12 

69 

0 

0 

12 

ro 

3.1^, 

70 

9' 

12 

71   5 

13 

80 

0' 

IS 

81 

^i 

13 

82 

0! 

13 

83 

^ 

13 

83   7 

U 

93 

1 

U 

94 

0! 

I4 

95 

5! 

14 

96 

2 

l4 

97   4 

i.5 

108 

0 

15 

109 

2 .15 

1  10 

71 

15 

111 

9 

15 

1  12   8 

16 

24 

o; 

16 

23 

0 

|16 

25 

o'l 

16 

26 

2 

16 

27   4 

17 

37 

5 

17 

59 

0 

17 

41 

0; 

17 

42 

0 

17 

43  0 

18 

154 

c 

18 

55 

H 

18 

57 

5! 

18 

59 

2 

lb 

-61   0 

19 

71 

5 

IV 

1  0 

^1 

i^^ 

76 

^i 

19 

78 

o| 

19 

79   2 

iO 

91 

0; 

,2(. 

92 

7' 

'20 

95 

01 

20 

97 

0: 

2C 

99   3 

bi 

208 

5 

^  i 

211 

M 

2] 

214 

C'l 

21 

216 

oi 

21 

217   5 

-22 

28 

0! 

2-^ 

32 

t 

j22 

35 

0 

22 

37 

o| 

22 

58   5 

23 

51 

7 

33 

54 

c 

^23 

57 

3 

-»  0 

59 

0! 

1 

1.1  r> 
-O 

62   5 

24 

To 

5 

24 

76 

c 

i34 

78 

5 

24 

83 

5*24 

85   5 

25 

96 

5i 

25 

300 

0I 

|25 

304 

0 

^ 

25 

507 

ol  25 

303   9 

25  322 

0 

26 

25 

I 

26 

27 

5i|2e 

31 

5J 

2c 

35   5 

27.  45 

0' 

27 

48 

ol 

27 

53 

2 

27 

57 

ol 

CO   0- 

28  72 

^i 

2b 

76 

5 

28 

82 

(> 

28 

85 

0 

2b 

83   2 

29  97 

5 

29 

40  3 

ij 

29 

407 

2 

29 

4i2 

0' 

'2S 

415   0 

30  426 

0; 

\so 

32 

5; 

3o 

56 

ll 

ol 

41 

5 

30 

44   5 

3i  55 

0 

]3i 

62 

0! 

31 

66 

0 

72 

0 

31 

75   0 

o2  86 

2 

1.2 

94 

^! 

97 

2 

3i 

5('3 

5 

32 

508   0 

335  16 

z 

•^  0 
J  J 

5^2 

1 

2 

0  0 

527 

0 

!3: 

34 

5 

33 

29      5 

34  47 

1 

34 

53 

5i 

59 

<^ 

65 

0 

34 

70   0 

35  r9 

C; 

.00 

85 

2; 

35 

94 

2i 

\iS 

602 

5 

55 

-05  5 

366U 

5 

3  ■ 

62  i 

5 

3C 

62g 

C' 

1.3  0 

35 

)Ot> 

40   5 

57  52 

o7 

57 

5 

57 

66 

2 

!0  J 

73 

5 

37 

78   5 

38  85 

0 

38 

94 

C 

3b 

703 

i 

'58 

7c  8 

5 

3c 

715   0 

39  723 

39 

733 

c; 

a  -' 

4i 

5 

0  - 

48 

S 

3V 

55   5 

4C 

)  53 

8 

4o 

67 

5 

1> 

73 

•t 

'k(- 

87 

-it. 

9^,   3 

i^5 


Jl  Table  giving  the  Side  of  a  Square^  equal  to  a   Square 
inscribed  in  a  given  Circle. 

The  first  and  third  c:>lumns  give  (he  diameter  in  inch- 
es, and  extend  from  G  to  49  inches  ;  the  second  and 
^fourth,  give  the  square,  or  side  of  the  stick  in  inches,  and 
eighths  of  inches.  The  first  nnd  third  cohjmns  at  the  ri^^ht 
hand  of  the  double  line,  are  the  same  as  tlie  lirst  mention- 
ed, except  they  commence  at  6-f^  and  extend  to  49y|- ; — 
the  second  and  fourth  columns  i^ive  the  square,  or  side  of 
the  stick  in  inches,  and  hundredths  of  inches. 


)  f 

^ 

'^w 

5 

X 

~ 

■     ^ 

Uu 

3 

v_ 

ff 

en 

1^ 

5 

ex. 
o 
of5 

■  a 

O 

5 

Z3 

re 

r-^ 

3- 
C 

0 

2 

(T' 

3- 

3 
d 

.  CO 

(T 

D- 

t/> 

ft 

^ 

cr. 

r^ 

i — 

'  cfi 

^ 

S" 

-3 

CA 

►^ 

«-3            0 

w 

o" 

>• 

C/l 

ro" 

O 

^ 

O 

fD 

3i 
0 

a 

^ 

"^ 

o 

"* 

£. 

" 

*^ 

" 

~ 

"* 

3- 

3 

^*" 

5' 

::; 

3* 

5" 

zz 

CTi 

**^ " 

3" 

^ 

** 

^  * 

Ci 

^■^ 

o 

o 

^ 

0 

-r 

3 

•I) 

VJ 

Cfc 

rr 

^ 

X 

3" 

3 

re 

0 

IT- 

2 

CO 

3 
en 

1    ^ 

4 

2 

28 

T9~ 

6 

b 

~5 

4 

59 

28 

5 

20" 

lo 

:           7 

4 

7 

29 

20 

4 

7 

5 

5 

30 

29 

5 

20 

85 

;     8 

5 

5 

30 

21 

2 

8 

5 

6 

01 

30 

6 

21 

66 

'     9 

6 

o 

31 

21 

7 

9 

6 

71 

31 

5 

22 

27 

1   10 

7 

0 

32 

22 

5 

10 

5 

7 

42 

32 

6 

22 

98, 

I  u 

7 

6 

33 

23 

2 

11 

5 

8 

•13 

33 

5 

23 

68 

'    12 

8 

4 

34 

24 

0 

12 

5 

8 

83 

33 

5 

24 

39 

'  13 

9 

1 

35 

24 

6 

13 

5 

9 

54 

35 

5 

25 

10    , 

14 

9 

7 

3ci 

25 

3 

14 

5 

10 

25 

36 

5 

25 

80 

15 

10 

5 

37 

26 

1 

15 

5 

10 

96 

37 

6 

26 

51 

1   16 

11 

2 

38 

26 

7 

16 

5 

11 

^Q> 

38 

5 

27 

22 

17 

12, 

0 

39 

27 

4 

17 

5 

12 

37 

39 

5 

27 

93 

18 

12 

6 

40 

28 

2 

18 

5 

13 

08 

40 

5 

28 

63 
34 

19 

13 

3 

41 

29 

0 

19 

6 

13 

78 

41 

5 

29 

20 

14 

1 

42 

29 

6 

20 

5 

14 

49 

42 

5 

30 

05 

21 

14 

7 

43 

30 

3 

21 

5 

15 

20 

43 

5 

30 

75 

22 

15 

4 

44 

31 

1 

22 

5 

15 

90 

44 

5 

31 

46 

23 

IG 

2 

45 

31 

6 

23 

5 

13 

61 

45 

5 

32 

17 

24 

17 

0 

46 

32 

4  , 

24 

5 

17 

32 

46 

5 

32 

88 

25 

17 

5 

47  33 

2 

25 

5 

18 

03 

47 

5 

33 

58 

26 

18 

3 

48133 

7 

26 

5 

18 

73 

48 

5 

34 

29 

^27_ 

19 

ol 

49|34 

5 

27 

5 

19 

44 

49 

ojSS 

00 

H 


OF  SURVEYING. 

Lantl  is  generally  mensurecJ  hy  a  Chain  of  GG  teet  in 
CMigth,  divided  into  lUO  equal  parts,  called  Links,  each 
Link  beinic  7,02  Inches  in  length.  A  Pole  or  Rod  is  iri. 
r!?et  or  25  links  in  length  :  hence  a  square  pole  contains 
272-^  square  feet,  or  625  square  links.  An  acre  of  land 
contains  \60  square  poles  or  rods,  and  435G0  square  feet, 
or  100000  square  links 

To  find  the  number  of  square  poles  in  any  piece  of  land^ 
^ake  the  dimensions  of  it  in  feet  and  find  the  area  in  squart. 
feet,  and  divide  this  area  by   43560,   the   quotient  will    h« 
the  nnmber  of  acres  ;  or  divide  by  272,25  and  the  quotien 
will  be  the  number  of  square  poles.     If  the  dimensions  b< 
taken  in  links,  and  the  area  found  in  sqiiare  links,  the  num 
l>er   of  acres  may  be   obtained  by  dividinj;   b^'  100000,    c 
which  is  the  same  thin^,  cut  ntf  the  five  riu;ht  hand  figures 
but  the  number  of  square  poles  miy  be  found,   by  dividiDj, 
by  625. 

PROBLEM  L  To  find  the  number  of  Acres  of  Land,  or 
the  number  of  Square  Foles^  in  the  form  of  a  regular  Faral 
Ulo^rani. 

RuLK.  MuUiplv  the  Base  or  Length  by  the  Perpendic- 
irL'T  Height  or  Breadth, ^nd  if  the  dimensions  were  taken 
in  Links,  divide  by  ^'Ib,  if  in  feet  by  272.25,  or  2721.  the 
quotient  will  be  the  number  of  Square  Poles,  which  tlivi- 
ded  by  160  gives  the  number  of  Acres. 

E>  AMPLF,.     Suppose  the  Base   be   60  feet  and  the  Per- 
pendicular 25  feet,  required  the  Area  in  Square  poles  ? 
Length  CO   feet 
Breadth  25  feet 
272,25)1500,00(5,5  Ans. 
1361,25 

138,750 
136.125 
PROBLEM   11.     To  find  the  numher  of  Acres   and  Poles 
ifi  a  piece  of  Land  in  thejorm  of  an  Oblique  Angulur  Paral- 
hiogram. 

Klle.  This  Area  may  be  found  in  exactly  the  same 
manner  as  in  the  preceding  problem,  by  multiplying  tb* 
••    >»  !."  ^[^'^  Perocndiculuf  height,  and  dividing   by  626  : 


^F  sunrrAiXQ. 


xyben  the  flimensions  are  tnkon  in  Link*  ;  by  272,25.  when 
faketi  in  feet,  the  quoiif;r.t  uili  oe  in  Amoricjn  i^oles,  woich 
divi<!e  "  bv  160  ^:iv<}>  the  •.  i.-uber  of  Acres. 

E  vpLK.  Siipjjosei'i  ?>•=<•  I^f' 63:J  Dnd  the  perpenfiic- 
Qlar  32o  Links  ;  required  the  number  of  rotes  ? 

Bn^e  632  Links  B.-^o  632  Links 


Perp. 


326 


Links 


3792 
1264 

1896 


Perp.  326  Lmk« 
3792 
1264 
1896 


«2a)206032(329,6  Poles. 
1875 

18.53 
a250 


Links  1,00000)2,06032 
in  an  Acre.  "       4 

24128 
40 


6032  9,651 2t)=to 

5625  2  Acres,  0  Roods,  and  ri^  Poles.. 

4070 
PROBLEM  in.      To  find  the  number  of  Acres  and  PoJ^ 
in  apiece  ef  Land  at  a  Triangular  fonn. 

Rule,  ^Multiply  the  Base  by  the  Perpendicular  height, 
aod  divide  the  product  by  1250  when  the  dimensions  are 
given  in  Links  ;  by  544,5  when  given  in  feet,  and  the  quo- 
tients will  be  the  answer  in  Poles. 

Xote.     Instead  of  dividing  by  1250,  you   may   multiply 
by  8  and  cutoff  the  four  right  hand  figures. 
Example.     Given  the  Base  AC  equal  to 
200  feet,  and  Perpendicular  BD   equal  to 
150  feet ;  required  the  Area  in  Poles. 
Perpendicular  150  feet 
Base  300  feet 

544,5)45000,0(82,6  Poles 
43560 

14400 
10890 

35100 

PROBLEM  IV.  The  three  Sides  of  a  Triangle  being 
given,  to  find  the  Area  Arithmetically. 

Rule.  Add  together  the  three  sides,  from  half  that 
sum,  subtract  each  side,  severally,  noting  down  the  re- 
mainders ;  then  multiply  the  Balf  suoa  and  the  three  remaifN 


OF  SVRFEYL\€f, 


ders  continually  together,  and  the  square  root  of  the  la-: 
product  \viil  be  the  Area. 

Example.  Suppose  a  Triangle  whose  three  sides  are 
;^0,  2o,  and  92. 

Sides,  30ri*25-|-22  sum  78-^2=30=— 30=9  and  39— 
26=13  atjd  39— 2-:=17,  the  half  sums  39x9x13X17= 
77571,  the  square  root  of  which,  is  equal  to  278,5  Chaiu?.. 
tr  27  Acres  o  Roods,  and  17,5  Poles. 

ON  THE  SLIDING  RULE. 

Example  in  Trigoxometiiy.     In  the  the  Oblique  Angu- 
?ar  Triangle  ABC.  let  there  be 
given    AB=56,  AC=d4,  angle  A 

ABC  46°  30',  to  tind  the  other 
Jingles,  and  tJie  side  BC.  la 
this  case  we  have  by  art,  53 
Geometry,  the  followins;  Can- 
ons ;  as  AC  64=Sine  zB  46° 
SO'  :  :  AB  5G  :  Sine  of  the  Ang. 
C,  to  the  Ans.  And  as  the  Sine 
/.B  :  is  to  the  side  AC  :  :  so  is 
the    zA   :   BC  ;     therefore    to 

work  the  fiist  proposition,  by  the  Sliding  Rule,  we  must 
bring  64,  on  the  Line  of  numbers,  on  the  fixed  part,  against 
46°  30'  on  the  Line  of  Sines  on  the  slider  ;  then  against  56 
on  the  tixed  part,  will  be  39°  24'  on  the  slider,  which  will 
be  the  Angle  C.  The  Angles  B  and  C  added  together,  and 
their  sum  being  subtracted  trom  180°.  leaves  the  Angle  A 
=94°  6',  Then  by  the  second  Canon  being  the  Angle  B 
=46°  30'  on  the  Line  of  Sines,  on  the  slider,  against  AC-«= 
€4  on  the  Line  of  Numbers  on  the  tixed  part  ;  then  against 
the  Angle  A=94^  6',  or  its  supplement,  85^  54'  on  the 
slider,  will  be  found  the  side  BC=o8  on  the  fixed  part. — 
In  a  similar  manner  may  the  other  propositions  of  Trigo- 
nometry be  solved  :  and  from  what  has  been  said,  it  will 
be  easy  to  work  all  the  problems  in  Plain  Sailing,  Middle 
L  ititude  S-iiiing,  and  Mercator's  Sailing,  as  in  the  follow- 
ing examples. 

Example  1.  Given  the   course,   sailed    1    point  and   the 
jsiance  85  miles  ;  required  the  difi'crence  of  Latitude  and 
De[»  nture  ? 

By  Case  Ist.  of  Plain  Sailing,  we  have  these  Canons  : — 


OF  SURVEYING.  «y 

As  Tlatlius  C.  points,  is  to  the  distance  C5,  so  is  the  Sine 
Compl.  ot  the  Cour5e=7  Poin,  to  the  Ans.  or  difference  of 
Latitude  :  and  as  Radius  8  points,  is  to  the  Distance  83  scr 
is  the  Sine  Course  1  Point,  to  the  Departure  ;  her.ce  we 
must  bring  the  Radius  8  points,  on  the  lixed  part  of  the 
Line  Rhombs,  against  85  on  the  Line  of  Numbers  on  the 
j^lider;  then  ajrainst  7  points  on  the  Line  Rhombs  will  be 
found  the  diffeWnce  ot  Latitude  83i  on  the  sUder,  and  a-^ 
gainst  1  point,  will  be  found  the  Departure  16^-  miles.  If 
the  Course  is  given  in  Degrees,  you  must  use  the  Lmc 
marked  SIN. 

Example  2.  Given  the  difference  of  Latitude  40  miles, 
and  Departure  30  miles  ;  required  the  Course  and  Dis- 
tance ? 

As  the  difference  Latitude  40,  is  to  the  Radius  45^,  so  is 
the  Departure  30,  to  the  Tangent  of  the  Course.  There- 
lore,  we  must  brins;  40  on  the  Line  of  Numbers  found  on 
the  slider  against  45^  on  the  Line  of  Tangents,  on  the  fix- 
ed part ;  then  against  30  on  the  slider,  will  be  found  the 
Course  37°  nearly. 

Again  ;  the  Canon  for  the  distance  given.  As  the  Sine 
Course  37°,  is  to  the  Departure  30,  so  is  Radius  90<^  to 
ihe  Distance.  Bring  37°  on  the  Line  of  Sines,  on  the  fix- 
ed part,  against  30  on  the  Line  of  Numbers,  on  the  slider  ; 
then  against  90°  on  the  Line  of  Sines,  on  the  fixed  part  will 
be  found  the  distance  on  the  slider. 

Example  3.  Given  the  middle  Latitude  Sailing,  we  have 
this  Canon.  As  the  Sine  of  Complement  of  middle  Lati- 
tude 50°,  is  to  the  Departure  30,  so  is  the  Radius  90°,  to 
ihe  difference  of  Longitude.  Bring  50°  on  the  Line  of  Sines 
on  the  fixed  part,  against  30  on  the  Line  of  Numbers,  on 
the  Slider  ;  then  against  90*^  on  the  fixed  part,  will  be 
found  39  on  the  slider,  which  will  be  the  difference  of 
the  Longitude  required. 

•  It  may  be  observed,  that  in  the  calculations  of  Spheri- 
cal Trigonometry,  the  Sliding  Rule  is  rather  an  object  of 
curiosity,  than  of  reu  use,  as  it  is  much  more  accurate  to 
make  those  calculations  by  Logarithms. 

How  to  find  the  Course  when  the  Base  and  Perpendicu- 
-lar  are  given. 

Rule.  First  find  the  Hypothenuse  by  the  square  root, 
then  add  one  half  of  the  Base  to  the  ilvpothenuse.     Then 

H2  '  ^ 


90  OF  SURVEYIXG. 

say,  as  that  Qumber  is  to  So,  so  is  the  PerpeRdicular  to  the 

Course. 

ExA-MPLE  1.    Run  North   100  Chains,   then   West   100 

Chains,  or  Links,  or  Teet,   or  yards,  or  miles,  or  any  thin^ 

else. 

\00         100         191,12  :  83*^  :  :  100 

lOO  ICh)  100 

"iuOOO    TUOOO     lai, 42)8600.00(44°    55'   38"      The 

10000  7650  8    'Course,  but  it  should 

300UO(141,42  Hvpoth.       943  20  ^^  ^'^''-    It' instead  of 

1  50    >-  Base  765  63  ^^"^  ^^  "  the  2d  term, 

^  96  60  sed,theAns.    wouKt 

have  been  45**  V 


L'Cl;400  1065120(56  2'/ nearly. 

9oi  9571UO 

-324} 11 900  3  0G020 
'll'296  95710 

-'8282)60400  12310 

56564  60 


3836  733600(38" 

57426 

164340 
153136 


1 1 204 
K.\A3i?LE  2.  Suppose  the  Base  80  and  the  Perpendica- 
;r  60  ;  what  13  the  Course  ] 

8 J         60  As    140  :  86,1-4  :  :  60 

80         60  60 

«;4U0     3600  H0)5168,40(36,917<' 

•>600  420  ^     60 

jOOO(100  ?r'ypothenuse  968         55,020 

iO..0O     40  haliEiLse  840  bO 

'VxJoSTTiO  1284  l,2uO 

r:*jO 


02 40  Ans.  36^  55'  1^'^ 
140 

Too 


ExAHFLE  for  finding  the  Base  and  Perpendicular.  If  yoa 
•jfl  North,  30?  East,  70  Rods,  wb^t  w  your  Perpendicular? 


OF  SURVEYING. 


SI 


1.  Rarliiis  Rods 
60,00  :  70  : 
•     30 


SO*^ 


60,00)2100,00(35  Rods. 
1800  0 

30000 
30000 


2   Rerersed 
Radius  Rods 
69,22  :  70  :  :  60® 
60 


QOOOO 


69,22)4200,00(60,67  Rods. 
4153  2 

46800 
41532 


52680 
48454 


A  Table  of  Natural  Radii. 


4226 


o 

Radii. 

o 
~24 

Radii. 

47 

Radii. 

0 

7C 

R 

'■i.  ■; 

bij 

880 

58 

986 

64 

240 

74 

544 

•2 

bQ 

922 

25 

59 

141 

48 

64 

563 

71 

.5 

105; 

3 

bQ 

967 

26 

59 

300 

49 

64 

895 

72 

75 

661| 

4 

bl 

017 

27 

59 

466 

50 

Qb 

238 

73 

76 

293i 

5 

57 

072 

28 

59 

637 

51 

65 

590  j 

74 

76 

942i 

6 

57 

130 

29 

59 

815 

52 

65 

950 

75 

77 

608; 

7 

57 

193 

30 

60 

000  1 

bo 

m 

323 

76 

78 

292; 

8 

57 

260 

31 

30 

190 

54 

m 

705 

77 

-n 
1  O 

994! 

9 

57 

331 

32 

60 

388 

55 

61 

093 

78 

79 

714, 

10 

o7 

407 

33 

60 

592 

56 

67 

502 

79 

i.O 

453; 

11 

57 

488 

33 

60 

804 

57 

67 

917 

80 

81 

21li 

\- 

57 

573 

35 

61 

021 

58 

68 

343 

31 

81 

990; 

13 

57 

664 

36 

61 

246 

59 

68 

781 

82 

82 

784 

14 

57 

757 

37 

61 

479 

60 

69 

231 

83 

83 

6£3 

15 

57 

857 

38  61 

719 

61 

69 

692 

84 

81 

4c2 

13 

57 

961 

39 

62 

967 

62 

70 

166 

86 

35 

317 

17 

58 

071 

40 

62 

222 

63 

70 

653 

86 

S6 

205 

i:. 

53 

180 

4! 

62 

485 

64 

71 

153 

87 

87 

116 

19 

58 

306 

42',u2 

617 

65 

71 

666 

88 

88 

0c2 

20 

58 

431 

43 

.33 

036 

QQ 

72 

193 

89 

89 

013 

21 

58 

562 

44 

•33 

323 

67 

72 

734 

90 

90 

ceo 

2  J 

58 

698 

45|63 

620 

68 

73 

289 

i 

23 
1  — 

58 

840 

46|63 

925 

69 

73 

859 

This  Table  extends  from  1^  to  90°,  and  is  made   by  the 
following 

Rule.     Divide  four  times  the  square  of  the  Comple* 


9?  OF  SURITAIXG. 

ment,  by  three  times  the  Complement,  add  this  to  309,  aad 
then  add  the  Angle  to  the  quotient. 
Example  1.  Given  10  Degress. 
90  .         80  540)25600(47,407 

^0  _3  2160      lOano;.  ordg. 

80  Conpleraent  77^  ~^^  57~K>7     Arrs. 

CO  300  3780 

6400  «q^-  Corap.  ^  Divisor  "i^uTo 

4  2160 

25600  Dividend  40,00 

Example  2.  Given  the  Angle  80  Degrees. 

00  10x3=30-i-3ub=330  10 

80  3 

10   Complement.  30 

10  300 

100  Square  of  the  Complement.  330  DivUofe. 

4 

330)400('1,212  to  which  add  the  Angle 
330^ 

"^00  1,212 

C60  80 


400  81,212   AGS. 

330 


700 
Application  and  Uee  of  tht  Radius  'Table. 

Given  the  side  AB=16,8  Pole,  Angle 
A=58o  to  find  AC. 

In  the  left  hand  column,  under  Deg. 
find  32,  and  against  it,  under  Radius  you 
will  find  60,4,  nearly. 

Then  as  60,4  :  32  :  :  AB  :  BC. 
16.8 

"336" 
504 

50,4)53776(8. &=Side  BC. 
4832 

5440 


OF  svrveylyg:  & 

Then  as  68,3-1  :  58°  :  :  16,8  ;  or  as  A  Radius  Is  to  Angle 
16,8  A,  so  is  the  Hypothenuse 

J  oil'  to  the  Perpendicular. 

840 
68,34)974,40('14,25    hC. 
6834 

29100 
27336 


17640 
13668 


39720 

So  that  if  one  Angle,  and  the  Hypothenuse  or  Course  is 
given  of  any  Right  Angled  Triangle,  the  Base  and  Per- 
pendicular, may  easily  be  tbund  as  above. 

Oblique  Angled  Triangles,  when  the  Angles  and  one 
side  are  given,  may  be  solved  by  the  table,  by  finding  the 
Pependicular. 

In  the  Obliqued  Angled  Triangle  giv-  B 

en,  AB=100  Miles  or  Poles,  Angle  A=  A 

60^  and   Angle    0=60^  ;  required  the  /,  \ 

Perpendicular  BD  ? 

As  60  :  30O  :  :  100  :  50  AD.  / 

As  69,231  :  60^  :  :  100  :  Ans.  / 

6000  ^  ^ i ^C 

1000  D 

69,23 1)600UOUO( 86, 666  BD  Miles,  or  it  may  be 
553848  called   Latitude,   or   De- 

461520  '  parture,  as  well   as   Per- 

415386  pendicular. 

461620 
415386 


459540 
415386 


441540 
fiote.     By    adding   any   two  Angles  of  a'  Triangle,  to- 
gether, and  subtracting  their  sum  from  180  Decrreo-*,   will 
remain  the  other  Angle.  Thus, in  the  Figure,  60HO=120, 
wbich  if  subtracted  from  180,  leaves  60,  the  Angle  B. 


S4 


OF  LOGARITHMS. 

The  usual  method  of  computing  the  Lo2;arithm«i  to  anj 
af  the  natiirai  numbers,  12  3  4  5,  kc.  is.  as  fc-iinw?  : 

Rule.  1.  Take  -.nv  two  numners  whose  ditTerenre  is 
iinit^,orl,and  let  the  Log.  to  the  lesser  nutnher  be  known. 
'"2.  Divide  ihe  constant  decimal  ,8G85C'8P64,  &c.  (or 
2-r£,3025,  ^c.)  by  the  sum  of  the  two  numbers,  and  re- 
serve the  quotient  :  divide  th"i  several  quotients,  bj'  the 
square  of  the  sum  of  the  tuo  numbers,  and  reserve  the 
qnoiient ,  .'ivitie  tins  last  quotient,  aiso,  by  the  square  of 
the  sum,  and  a^ain  reserve  the  quotient  ;  and  thus  proceed. 
continuallv  dividing  the  last  quotient,  by  the  square  of  the 
sum  of  the  two  uumbers,  as  long  as  division   can  be  made. 

3.  Write  these  quotients  in  their  order,  under  one  an- 
other, the  first  uppermost,  and  divide  respectively  by  the 
prime,  or  odd  numbers,  13  5  7  9  11  13,  &:c.  as  long  as 
division  can  be  made,  that  is,  divide  the  first  reserved  quo- 
tient^by  1,  the  second  by  3,  the  third  by  6,  the  fourth  by  7, 
and  so  on. 

4.  Add  all  these  last  quotients  together,  and  their  sum 
will  be  the  Logarithm  of  the  greater  number  by  the  less'; — 
to  this  Logarithm,  add  the  Logarithm  of  the  lesser  number, 
and  their  sum  will  be  the  Logarithm  to  the  greater,  or  pro- 
posed number. 

Example  1.  Let  it  be  required  to  compute  the  Loga- 
rithm of  the  number  2.  Here  the  given  number  is  2,  and 
4he  next  less  number  is  1,  (whose  Lo2;arithm  is  ,0000,)  and 
the  sum  of  2  and  1  is  3,  whose  square  is  9. 


3)868588964 

1)289529654 

289529654 

9)289529654 
9)32169962 

3)32169962 
5)3574440 

10723321 
714888 

9^3574440 

7)397160 

56737 

9)397160 

9)44129 

4903 

9)44129 

9)4903 

9)545 

11)4903 

13)545 

15)61 

446 
42 

4 

9)61 

,301029995 

Add  Log.  of  1 

.  ,000000000 

True  Log.  of  2  ,301029995  Ans. 
Ex.\MPLEi  2.     Let  it  be  required  to  compute  the  Lo|£[/ 


OF  LOGARITHMS. 


^y 


lithrn  of  3.  Here  the  given  number  is  3,  jind  (he  next  le.is 
l^  2,  whose  Lo-iiiithm  i>y  the  rirst  example  is  301029095, 
and  ihe  ?um  of  2  and  3  is  6,  and  the  «qaare  of  which  is  .25. 


5)868588903 

2^5)173717703 

25)0948712 

25)^77948 

25)11118 

.25)445 

25)18 


1)173717793 

3)0948712 

5)277948 

7)11118 

9)445 

11)18 

Add  Loo;,  of  2 


173717793 

2316217 

65590 

1528 

50 

2 

,1760912*00 
,301029995 


L^iarithm  of  3,  477121198  Am. 
As  the  sum  of  the  Logaritlmis  of  numbers  gives  the  Log- 
nrithm  of  their  product,  and  the  ditTerence  of  the  Loga- 
rithms gives  the  Logarithm  of  the  quotient  of  their  num- 
bers. From  the  above  two  Logarithms,  and  the  Logarithm 
of  10  which  is  1,  we  may  raise  a  great  many  Logarithms,  as 
in  the  following  examples. 


Example  3. 

2x2=4  therefore  to  the 
Logarithm  of  2,  ,301029995 
Add    Log.  of  2,   .301029995 

Loa(.iritiim  of  4,  ,602059980 
Example  5. 

2x4=8  therefore,  to  the 
Log.  of  2,  ,301029995 

Add  Log.  of  4,      ,602059990 

a.     ithmofS,    ,903089985 
['  Example  7. 

5x8=40  therefore,  to  the 
Log.  of  6,  ,903089985 

Add  Log.  of  5,         ,698970005 

Log.  of  40,  T,602059990     Log.  of 320,  2,505 1499.7» 

Aad  thus  computing  by  thiS  general  rule,  the  •Logarithms 
of  the  prime  numbers,  13579  11  13  15  17  19  21 
23  25,  &;c.  and  then  by  using  composition  and  division,  we 
m;»y  easily  find  as  many  Logarithms  as  we  please,  or  exam- 
ine any  in  the  Table. 

Directions   for   Uiking   Lftganlkm^,  and  thcit  Knfnhcrs 
from  the.  fhbU.. 


Example  4. 
2x3=6  therefore,  to  the 
Log.   of  2,  ,301029995 

Add  Log.  of  3,    ,477121256 

Log.  of  6,  ,778151250 

Example  6. 

10-r2=5  therefore,  fronr. 
Log.  of  10,  1,00000000( 
take  Log.  of  2  0,301 02999i 

Log.  of  5,       0,69897000*, 

Example  8. 

8x40=320  therefore,   to 

Log.   40,        1,602059990 

Add  Log.  8,  0,903080985 


96  OF  LOGARITHMS. 

Look  for  the  number,  whose  Logarithm  is  required,  m 
the  Column  of  Numbers,  and  against  this  number,  its  Log- 
arithm will  ho  found. 

Thus;  the  Logarithm  of  1234  is  3,0913151  ;  so  that  a- 
ny  number  less  than  10000  may  easily  be  found  in  the  full 
Table  by  inspection. 

But  if  the  number  is  greater  than  10000,  and  less  than 
10000000,  rut  off  four  figures  on  the  left  of  the  given  num- 
ber, and  find  the  Log:irithm  in  the  Table  ;  add  as  many  u- 
nil"?  to  the  Index,  as  there  are  figures  rematning  on  the  right  ; 
subtract  the  Logarithm  found,  from  the  nest  following  it  ; 
then  as  the  (Ufference  of  numbers  in  the  Canon,  is  to  the 
tabular  distance  of  the  Logarithms  answering  to  them,  so 
are  the  remaining  ti<£ures  of  the  given  number,  to  the  Log- 
arithmic difference  ;  which  if  it  be  added  to  the  Logarithm 
before  found,  the  sum  will  be  the  Logarithm  required. — 
Then  let  the  Logarithm  of  92375  be  required.  Cut  off 
the  four  tiist  figures,  9237,  and  to  the  Index  of  the  Loga- 
rith.m  corresponding  to  them,  add  one  unit,  because  one 
riiiure  is  cut  off,  on  the  right.  Then  from  the  Logarithm 
of  the  next  greater  number,  9238=3,9655780,  subtract  the 
Log.  of  the' given   number,  9237=3,9055309 

Indes=10  ;  then*  as  10  :  471  :  :  5=unit 
added  to  4==to  the  Index  of  the  Logarithm,  corresponding 
to  them  ;  because  one  figure  is  cut  off,  on  the  right  hand, 
and  the  Answer  w'ill  be  235,  which  added  to  the  Logarithrai 
4, 655309-j-235=4, 9655544=10  the  Logarithm  required. 

Or,  more  briefly,  find  the  Logarithm  of  the  first  four 
figures,  as  before  ;  then  multiply  the  common  difference, 
which  stands  against  it,  by  the  remaining  figures,  of  the 
given  number  ;  from  the  product,  cut  off  as  many  figures 
at  the  right  hand,  as  you  multiplied  by,  and  add  the  re- 
mainder to  the  Logarithm  before  found,  fitting  it  with  a 
proper  Index  ;  as  the  Index  must  always  be  one  less,  than 
the  number  of  figures  in  the  given  natural  number  ;  so  the 
Index  of  the  Logarithnn  for  any  natural  number,  less  thaa 
10,  must  be  0  ;  and  for  any  number  between  10  and  100, 
the  Index  will  be  1,  and  from  100  to  1000,  2  and  so  on. 


*  If  one  figure  is  cut  off,  say  as  10  h  to  the  diflference  of  the  Log;- 
•rithra  ;  if  two  figures  are  cut  off.  as  100  is  to  the  difference;  if  thre«. 
t'\!?u  say  as  1000  is  te  the  difference,  &c. 


or  LOGARmiWJ.  97 

The  Logaritlini  of  a  decimal  iVacfion,  is  the  same  as  that 
of  a  whole  number,  excepting  the  Index.  Taiie  out  then 
the  Logarithm  of  a  whole  number,  coDsiisting  of  the  same 
figures,  observin}^'''to  make  the  negative  Index  equal  to  the 
distance  of  the  lirst  signiricant  figure  of  the  fraction,  froni 
the  place  of  units.  Example. 

The  Loz.  of  0,07643       is  2,8852639  or  8,8832639 

0,00259       is  3,4132998  or  7,4132998 

♦*  "  0,CQ0G278  is  4,7978313  or  6,7678213 

To  find  the  Los^arithm  of  a  mixed  Decimal  Fraction. 

Find  the  Log/uithm  in  the  same  manner,  as  if  all  the 
Sgures  were  integers  ;  and  then  prefix  the  Index  belong- 
ing to  the  integral  part.  Thus,  tlie  logarithm  of  39,68  is 
1,5985717,  here  the  Index  is  1,  because  1  is  the  Index  of 
the  Logarithm  of  every  number  greater  then  10,  and  less 
than  100. 

Tofnd  the  Losarilhrn  of  a  Fuls^tr  Fraction. 

Subtract  the  Log.irithm  of  the  demoniinator  from  that  of 
the  numerator,  an(i  the  difference  will  be  the  Logarithm  of 
the  fraction. 

V^hat  is  the  Lo-arithm  of  |^  ? 
Logarithm  of  37,  1,5682017 
Logarithm  of  94,  1,9731279 

1,5950738  when  the  Index  i*:  negative. 
Tofnd  the  JVatuj'al  JVuinber  to  any  Logarithm  iii  the  liable, 

Tiiis  is  to  be  dene  hy  the  reverse  of  the  former,  viz.  by 
sear^tjing  for  the  proposed  Logarithm  those  in  the  table, 
and  taking  out  the  corresponding  number  by  inspection,  in 
which  the  propf.T  number  of  integers  is  to  be  pointed  off, 
viz.  one  more  than  the  units  of  the  atiirmative  Index. 

To  find  the  A\iTnher  corresponding  to  a  Logarithm,  great' 
er  than  any  in  the  Ihble. 

Frst,  subtract  the  Logarithm  of  10,  100,  1000,  or  10000 
from  the  given  Log.  greater  than  any  in  the  table  td!  you 
have  a  Logarithm  that  will  come  within  the  compass  oi  the 
table  ;  then  tii-.o  the  number  corres{)oading  to  this,  and  mul- 
tiply it  by  10,  100,  1000,or  10000  the  product  will  be  the 
numb.^r  required.  Suppose  the  number  corresponding  to 
the  Logarithm  of  7,7589875  be  required.  Subtract  the 
Logarithm  of  the  number  lOGOO,  which  is  4,0000000  from 
7,7589875,  there  remains  3,7589875,  the  natural  number 

I 


«»g 


OF  LOGARITHMS. 


rorresponrling  to  which  is  6741  ;  this  mullipliefl  by  lOOOO 
f^ives  tiie  ijimiber  aiisivvering  to  the  given  Logarithm 
='574iOUUO. 

MULTIPLICATION  BY  LOGARITHMS. 

Multiplication  is   per'';rmed   b}'   takinsj  from    the   table, 
Logijrithms  answeriug  to  both  factors,    and   their   «imi  will 
he  the  product  in  Logarithms,   the    number  answering   to 
which,  wiii  be  the  answer.     Multiply  45  by  27. 
Numbers.   Logarithms.  Numbers.  Logarithm*. 

46  L  6532 125  23,14  l!3643G34 

27  1,4313638  76.99  1,8807564 


1215 


3.'JG45763 


1 


:,86 


3,2151198 


Multiply  3,686,  0,8372,  0,0294,  2,1046,   and   add  them 
toschther. 

Here  the  2  to  be  carried  from 
the  decimals  to   the   Index. — 
Cancel  the    2,   and   there  re- 
mains 1  io  be  set  down. 


Numbers. 
3,586 
2,1046 
0,8372 
0,0294 


Logarithms. 
0,5646103 
0,3231b96 
1,9228292 
2,4683473 


C, 185768        l,26C95o4 

Practical  Exampe.     What  cost  87  pounds  of  green  tea, 
at  j552,12  per  pound?  Numbers.     Logarithms. 

2,12  0,3263359 

87  1.9395193 


$184,44  2,2658542 

DIVISION  BY  LOGARITHMS. 

Rule.  From  the  Logarithm  of  the  dividend,  subtract 
the  Logarithm  of  the  divisor,  and  the  number  answering  to 
the  reuii.irjder,  will  be  the  qiiotient  required. 

Examples.       Divide  15811  by  165,  and  163  by  8,18. 

Numbers.     Logarithm  Numbers.    Looatithms. 

Dividend    15811        4.1989593     Divd.      163       2,2121876 

Divisor  163       2,2121876     Divi.     8.18       0,9127533 

Quotient        ~0f       1,9867717     Quo.  19,926        1,2994343 

PROPORTION,  OR  RULE  OF  THREE  BY  LOG. 

Rule.  If  the  proportion  be  Direct,  add  the  Logtrithms 
of  the  second  and  third  terms,  and  subtract  from  their  sum, 


OF  LOGARITHMS.  d\) 

flie  LOi^arithm  cf  the  first  term,  the  remainder  will  be  the 
term  ofthe  Logarithm  required. 

ITlhe  proportioD  he    Inverse,  add   the  Logarithms  of  the 

first  and  second   term?,  and   froDi  their  sum,  subtract  the 

Logarithm  ofthe  third  term  :  the   remainder  will   be    the 

Logarithm  to  the  required  term. 

Example.  Find  a  fourth  proportion  to  7964,  378,  27960. 

Numbers.  Logarithms.       Numbers.   Logarithms. 

2d.  term      378      2,5774918  7,0240290 

3d.  term  27960      4,4465372   1st.  Uam  7964      3,9011313 

7,0240290  4th.  term  1327       3,1228977 

Practical  Example,     if  6  jards  of  cloth  cost  g5,  vvliUt 

will  20  yards  cost  ? 

As  6  Log.  0,77815 


is  to  5  Log-  0,69897 
so  is  20  Log.  1,30103 

Sum  of  2d  and  3d  2,00000         The  answer,  therefore  is 
Subtract  first  6        0,77815  iq  dollars  and  |^  or  16 

Ans.  16,67   Log.     1,22185         dollars  and  67   cents. 

EVOLUTION  BY  LOGARITHx^lS. 

Rule.  Divide  the  Logarithm  of  the  number  by  the 
Index  of  the  Power,  the  quotient  is  the  Logarithm  ofthe 
root  sought.  But  if  the  power,  whose  root  is  to  be  extrac- 
ted is  a  (ieci  nal  fraction,  less  than  unity,  prefix  the  In  iex  of 
its  Logarithm,  a  figure  less  by  one,  than  the  Index  of  the 
Power,*  and  divide  the  whole  by  the  Index  ofthe  Power, 
eind  the  quotient  wll  be  the  Logarithm  ofthe  root  sought. 

Example  1.   What  is  the  Example  2.   What  is  the 

square  root  of  196  ? .  cube  root  oi  27  ? 

196  Log.  2)2,29226  27  Log.  3)1,43136    ' 


Ans.    14  Log.      1,14613  An^.    3  Log.      0,47712 

Example  3.   ^Vfiat  is  the  Example  4.   Vi'^hat  is  the 

square  root  of  40,96  ?  cube  root  of  0,015625 

40,93  Log.  2)1,61236  0;015625  Log.  8,19382 

Ads.  6,4  Log.  0,80618       P'^^fix  2  Index,  3)  28,19392 

Ans.  0,25  Log.  9,39794 


*  In  Ihis  rule   it  is  s'lpposed  thit  10  was  borrowed  in  finding  the 
idex  of  the  decimal,  according  to  the  rule.     Ta^e  07. 


!0' 


I.OGxiRITHMS 

OF  THE   NUMBERS,   FROM 
1   to  100. 


No.  1 

Lo-.    N.l 

Loc..   ( 

N. 

Lo-. 

N. 

Log. 

—l\ 

J.  000000 

26 

1.4149731 

bl' 

1.707570 

76 

1.880814 

2 

301030 

27 

431364 

52 

716003 

77 

886491 

3 

477121 

28 

447158 

53 

724276 

78 

892095 

4 

G020G0 

29 

462398 

54 

732394 

79 

897627  i 

i 

698970 

30 

477121 

55 

740363 

80 

903090  . 

( 

778151 

31 

491362 

56 

748188 

81 

908485 

1 

845098 

32 

505150 

57 

755875 

82 

913814 

8 

90309(' 

33 

518514 

58 

763428 

83 

919078 

9 

954243 

34 

531479 

59 

770852 

84 

924279 

10 

l.OOOOOC 

35 

544068 

60 

778151 

85 

929419 

1  11 

041393 

3G 

556203 

61 

785330 

86 

934498 

:  12 

070181 

37 

568202 

62 

792392 

87 

939519 

!  13 

113943 

38 

579784 

63 

799341 

88 

944483 

!  14 

146128 

39 

591065 

64 

808180 

89 

949390 

!  15 

176091 

40 

602060 

65 

812913 

90 

954243 

1  16 

204120 

41 

612784 

66 

819514 

91 

959041 

:  n 

230469 

42 

623249 

67 

826075 

92 

963789 

18 

255273 

43 

633468 

68 

832509 

93 

968483 

^  19 

278754 

44 

643453 

69 

838849 

94 

973128 

;  20 

301030 

45 

.653213 

70 

845098 

95 

977724 

•  21 

322219  46 

'662758 

71 

851258 

96 

982271 

•  29. 

342423  47 

672098 

72 

857333 

97 

986772 

\   23 

>      361738',  18 

681241 

73 

863323 

98 

991226 

1  24 

380211 

19 

6901 9f 

74 

869232 

99 

995635 

!  9r 

•   39794C 

5C 

69897r 

75 

875061 

100 

2.000*.  00 

A  TABLE  OF  LOGARITHMS.  IQl 


i 

'a 

r-i  TT  lo  CO  o  CO  CO  i-<  CO  c;;  o»  o  -^  -^  o  C'":  o  tj<  s^  Ci  co  t  g^  ■ 
-T.  r-  ^  '^  i>  cr;  1--  c<  G<  cr.  Ci  CO  CD  G-?  G!  CO  i~-"  ^  CO  1— 1  c^  O  O 

CC    '-<    -*   O   t-   OO    O-J    O    O   C^'   Ci    CO   CO   -C   CO    O   CO    O   '-1   CO   **    O    1-0 
ro.   CO  OJ   CO   O  ^  CO  CO   1--   O   '^  OO  C^  O  O   -^   1:^  '-'  ^  CO  G^  CO  CTi 
2O'-''-<0^G-«G^C0C0'=^'=*'^OOC0C0C0i>i>l>C000C0 

CO 

.—  CO  GO   t-   --1   CO   r-r   Ci  CT;   G^<   O  Ct   C:  C-f   G^   CTj  C'O   O  CO  i--   I-   i>   c,-) 
CO^cr;OCOC;;l>— 'G^(0'^'T0■^■^0-P'T1— 'OCOTTCO 
-tr   l>  Ci   »-<  CO    '^   ^0   CO   CO   CO    »-0    -^  CO   '-^  Ci    t^   -^   -^   OO   -^   O  CO   1-1 
CO    t~   '—   CO    O    -^   CO   CJ    CD    O    -^   CO    CNf   CO   Oi   CO    t-    '-'    ''T   CO    G'J    O   O 
O   O   '-'   "  G<   G-<   G-J   CO  CO   '^   -^   ^   uO   O  lO  CO  CO  i>  l^   i>  CO  CO  CO 

q 

I- 

c;.  T-  c;   ~    i-  'O  "*  CO  O  i--  CC'  CO  -^  O  Ci  CO  '—  CO  '-'  'T'  }>  '-'  >-0 
■JJ   Gn(    1--   i>    rr   t^  CO   >— 1   CO    O    "^    O   G^^   CO   CO   CO    1>   l^   >0   C:    O  C>  rf 
O  GO   LO   t^  C-   O  '-I   C>J   G-^   ©?   '-'   O  Cj  r^   LO  CO   O  J>   -^   O  t-  G*   CO 

CO  1^  -^  >o  o  "T'  CO  e»  CO  o  '^  CO  i-<  uo  cj  CO  i>  o  ^  CO  T-'  liO  CO 

O   O   1—  '-'   '-'  e<   G^   CO  GO   -^   "^   '^   ^  O   O  CO  CO  t-  l^  t-  CO  CD  CO 

CO   '^   C^   C::>  G-*   'T   1--   G<   O  '-'   O   T-'   CO   CC   'O.CO  c;  t^  lO   '— >   £>   -^   O 

C-.  cr.  rr  CO  GO  CO  1^  '—  co  >—  o  co  co  t^  co  i-O  c;  O  co  go  ■^  C'O  C5 

O   CO   — .   CO    O   CO    t-   CO   CO   CO   i>   CO    >-0   CO    '-'   CTj   CO    TT    C    t-   CO   C5    rf 
->'   CO  -r-,   i_o  cr.  CO   t^  »->   "^  en   CO   i^  -^   O   C^  G^  CO  O  '7"   t^  '-'   '^  CO 
^   3   ^   ^   „   G^   Q^  CO   CO   GO   -^   rr   O  »^   ^  CO  CO  t-   t-  i>  CO  CO  CO 

«-0 

CO   CO   G^J    O   O    G?    O   CO    O    ^-   G-J    »-0   CO   CO    O   G'   CO    CO   CO   00   t-   CO    CO 
'-0  CO   G<   -r  T-'   >-0   O   O  c:   '—  CO   i>   >^:   Ci   O  CO   G-<   CO   '-^  CO   CO   l-  co  i 
'-<   rt«   O   C^   '—  ©,»   CO   -^   "^   -^  CO   3<   1— 1  C^  CO   lO  CO  O   t>  CO  Cj   »0  --n 
C-^   CO   O   -^  O   CO   l^  ^-i   >-^  Cr.   CO   t~-  ■»-'  '^  CO   GJ   CO   O  GO   t^   O  -^  CO- 
O   O   >—   ^   '-'   G »  0<   CO   CO  CO   "^   "C   ^   -0   »-0   CO  CO   t--  t^  t-  CO  CD  CO 

't' 

-r^  CO  O  — <  O  '-''  C  'T  c:  I-  c:  -::  ':o   :o  co  co  cO  c;  Gsf  ^  co  c^  t— 
c;   CO   w    GJ   O   -^"   -^   O  C<   "^  CO'   CO  CO   •->   3^   O   --O   CO   i-O   O  C^<   «  CO 
L-   O   CO   lO   I-  CO  C:   O   O   O  CTj  CO  t--  CO   ^  G^  CDj  CO   CO'   O  CO   Gs'   i-  1 
—  CO   O  -^  CO  G-f  CO  "  i-O  C;!  G-*  CO   O   •*  CO  G<  to  cr:  CO  t--  O  -^  i^  ' 
O  O  "  r-.  T-n  O^   G-(   GO   CO  CO   '^   -^  »-0  1-0  uO  CO  CO  CO   L-  £>  CO   CO  CO  ■• 

^                                                                    i 

G>                                                                                                                                              ! 

0^ 

'--'  C  CO  O  "^  G(  CO  w  CD   C-  w   1^-  O  O  w  C^'  ;o  CO  '^  O  CO  ■•— '  CO 
O   O   i^   O   CO   G-!   CO    w   C^   G^    L-   O-j   CO   C0>    -^   G-»   CD  CX'   CO    ':!<  CO   CO   G/ 
CO    -O)   CO    >— 1   G^*   -^   lO    -4D   CO   CO    iJ:S   TT   CO   Gv/    O   CO   »-0   OJ   C:    CO   G-*   CO   'Cf 
'-   »-0  C:j   -*  CO  CO  CO    O   "^  CO  &J    'Oi  O   -^  CD   T-i   lO  C'.   e(   CO   O  GO  t-  i 
3    O   O   '-  '-'   G-«   G-J  GO   GO   'CO   "^r   ■'^r'   O   ^   »-0  CO  CO  CO   I-  1>  CO  CD  CO  , 

<^             -              _        ' 

( 

:o   1-i  r-,   O  CO  CO   »-0  O  L-^  CO   G-)   >C  GO   "-0  CO  CM  CO   CD   t--  CO   -^   CO   ^• 
CO   CO   lO   CO  CO   ^   3-i   C:i   G{   G^  CO   O  CTi   •Tf  CO   UO   O  C^!    '-<   t--  O   O  i> 

CC  t-i  -T  CO  CO  o  '-'  "  e^i  G<  —  1— .  ci  CO  CO  rr  0-^  c-^  CO  o?  CI  lO  o 

Q    uO  C-:    CO   r~   G?   CO    O   -^  CD    G^   CO   CTi   so    «---   '-»   O  CO   G<   CO  CT5   CO    }>   1 
CD    O   O  '-1  T-.   GV  G^   CO   CO  CO   '^  '^r   **   ^   O  CO  CO  CO  f-  f>  t-  CO  CO   j 

-T  '— '  -0  c:  T--  .  ,  o  w  CO  i-O  t-  T  CO  CO  CO  it:  gj  i--  c  c>  co  ^  co 

:0  "^  <>«  O  O  C  -— '  CD  C>  G^  X  T-i  C  CO  CO  L--  CO  lO  O  —  ■^  'rr-  i— 

rj'  t^  CD  o<  rr  -o  t^  L^  CD  CO  i--  i>  c::  -^^  G-J  O  CO  JLO  G^'  cr.  i.O  »—  i-^ 

CTJ  -^  CD  CO'  t^  '-<  LO  Ci  CO  t-  ■r-i  LO  CD  GO  i>  '-'  TT"  CD  G^  »-0  C:;  CO  CO 

OOC-^r-iGJG^JG^  C0C0-V'T''^'-0»^COCOCOi>i>i:-COC0 

—J 

GJ 


Q  1-^  C  t^  CO  CD  w  rr  -^  '■O'  CO  CO  CD  CO  --O  CO.  CO  w  G<  l-  T-<  uO  O 

O  G^»  O  CO  C"D  CO  O  CO  G^>  G-(  CD  G-«  r-i  t-.  O  CD  O  00  CD  ■*  CC  CO  CO 

Z:  CO  CO  CO  cii  1-1  CO  CO  '-r  -^  CO  CO  G-<  o  cr^  CO  ^  -^  CO  o  ^  t^  n 

C?  rr  CO  Gi  t--  —  lO  C5D  CO  t-  — '  lO  CD  CO  CO  O  "^  DO  '-'  LO  CD  O!  CO 

^  O  O  T-H  ^^  G-}  C<  G^  CO  GO  'f  ^^  -^  O  iOi  i:0  CO  CO  t^  l^  1>  CO  CO 


g  i?  :2;  ,'-9  ^  ^  S  ??  3  ^  ;il'  £}  '^  >-'■•■  -■-'  t^  co  05  p  —  g^ 


}02 


A  TAELF.  OF  LOGARITHMS. 


•  _ 

3> 

zz. 

3* 

..» 

r^ 

^. 

^ 

;^- 

i.~ 

— 

c> 

c: 

7^ 

— 

c 

2^ 

_ 

•■J 

3, 

^ 

TT 

^- 

'  {:>• 

^ 

'^J 

tC, 

C- 

kc 

^ 

■»— 

-^ 

*  • 

cc 

— 

^ 

^ 

t^ 

^ 

v» 

— 

CC 

zz. 

;^ 

;^ 

ij^ 

'  C^ 

iSl 

~ 

— r 

zz 

C'* 

^ 

C; 

E  •■ 

tTX 

c^ 

c^ 

5» 

■f 

o 

i> 

cc 

^^ 

c; 

~ 

^ 

^ 

^ 

—  i  ^. 

^ 

~ 

Z  * 

l^ 

^ 

ot 

;^ 

^ 

C^ 

c^ 

^ 

C^ 

't^ 

c: 

<v 

iC 

■cc 

•— 

^ 

cc 

^— 

rr 

i-T 

" 

~ 

^^ 

"*^ 

S^ 

Cr* 

2-* 

• 

r: 

r: 

* 

' 

"^ 

rr 

■^ 

»C 

•-C 

'"' 

^•^ 

1  ""^ 

tC 

— 

C". 

^.— 

"Tc" 

o 

;;; 

»::; 

^ 

-^ 

:^ 

"3 

•^ 

^ 

~ 

i>" 

7^ 

-^ 

cc 

"5r 

~ 

cc  > 

i-' 

^— 

cc 

■^ 

c^ 

— • 

r^ 

^ 

»-• 

^ 

i!; 

c. 

^ 

cc 

■»t" 

cc 

.^ 

^ 

^ 

s-» 

•^ 

tc 

*-> 

't- 

3^' 

^ 

•^— - 

T  ~ 

ct 

C'' 

C;_ 

^. 

■-^ 

■r:^ 

cc 

ct 

^ 

c 

'Z 

t^ 

^ 

"';^ 

t- 

t> 

£> 

t- 

•o 

c^ 

c^ 

'-C 

c~. 

c^ 

^ 

•3^ 

C^ 

w" 

■c; 

3> 

r^ 

^. 

3« 

»C 

" 

— 

rr 

t- 

^ 

■r^ 

Z'. 

c. 

o 

^- 

^ 

»— 

"— 

— 

©5 

G< 

s* 

.G^ 

*^ 

c; 

— • 

r~ 

rr 

4^ 

c^ 

»c 

^ 

c^ 

„ 

»-• 

' 

I 

S/ 

— * 

.->. 

» 

-^. 

^_ 

— 

— 

-  - 

~z^ 

«» 

— 

— - 



"TT~ 

.^ 

— 

__ 

T^ 

— - 

— 

K^ 

t^ 

■•". 

t— 

^, 

!■— 

•rr 

r^ 

cc 

I> 

7^ 

t^ 

CC 

X 

7^ 

1- 

~ 

^ 

t-- 

rj 

t:; 

;^ 

"^ 

7^ 

^ 

;•■; 

i^ 

— 

•J^ 

^ 

^» 

;j; 

cc 

^ 

7^ 

^ 

t- 

~ 

^ 

— — 

'^i 

ZZ 

-f 

-^ 

T 

-r 

--.;;< 

i_f^ 

* 

^  1 

•^ 

^^ 

^> 

-■* 

"^ 

O' 

•  — 

*^ 

t^> 

t!; 

^z 

—  « 

jj^ 

^^ 

w 

^-^ 

£^ 

*"■ 

7*^ 

Is 

c; 

~ 

Z^ 

c 

c 

— 

— 

— 

3  J 

3J 

5' 

7^ 

r: 

r^ 

— 

-r 

-r 

^ 

^ 

^E 

'■^ 

~~ 

hi 

. — 

~- 

— 

— 

_ 

_ 

^— 

-- 

•- 

_«" 

^ 

„_ 

— 

^ 

.  — 

-^ 

— 

"c_r 

— 

_ 

' 

— 

r; 

C-- 

^-; 

-7- 

^ 

— 

r^ 

~ 

^ 

-^ 

"3 

lT, 

I^ 

'~ 

zz 

^ 

^ 

~> 

^ 

;^ 

^-^ 

,  ^ 

»:^ 

^ 

-f 

;; 

~  J 

"^ 

~ 

c-5 

.SI 

;^ 

^ 

Z'i 

r^ 

;^ 

l> 

zz 

Ci 

"^ 

— 

»— 

— 

—  [ 

._,    ;;t5 

iC 

zz 

y> 

^ 

^ 

5  > 

^ 

ct. 

3» 

i/:; 

Cl 

3~» 

iC 

CC' 

•^ 

-^ 

t- 

— 

rr 

t^ 

^ 

7^ 

2> 

Cl 

— 

^ 

■^ 

G^ 

S'-' 

2* 

"" 

•^ 

"^ 

TT 

TT 

•^ 

^ 

iC 

l:; 

" 

.  "-^ 

^ 

~^ir 

^_ 

— 

;■- 

— 

__ 

-- 

-  - 

__ 

'N^. 

— ^ 

-- 

-»- 

— 

— - 

J^ 

~"7" 

u 

'■~_^ 

vf 

-^ 

~ 

^ 

^ 

e^ 

— 

"* 

^~ 

cc 

2-> 

~^ 

c^ 

^ 

»-^ 

t> 

»^ 

i-^ 

~ 

Z:; 

t^ 

•^ 

— 

t^ 

^ 

»C 

~ 

^) 

tc 

^ 

C^ 

t;- 

•> 

Ct 

^ 

r^ 

-7- 

0 

*^ 

l> 

zz 

cc 

CC 

c^ 

^  '  — _ 

v^ 

CD 

Of 

«^ 

cc 

~  / 

ij; 

zc 

S-i 

^ 

C;; 

>— 

-J^ 

cc 

— 

TT 

»>. 

'■' 

fi 

** 

c; 

^* 

f  -«. 

Ci 

^ 

^ 

~ 

^ 

— 

— 

— 

^< 

3< 

o< 

7^ 

^ 

""^ 

^ 

rr 

—^ 

ij^ 

_^ 

-^ 

^ 

to 

-.    t 

'" 

iO 

^ 

c; 

r- 

— 

^ 

<^ 

^ 

»c 

2^ 

'■C. 

~ 

^ 

"<?• 

f^ 

73" 

^ 

r~ 

— 

;^ 

^. 

c^ 

-r 

P_ 

c# 

— • 

-^F* 

^ 

*■  — 

y^ 

j> 

-^ 

-^ 

1^ 

— ^ 

^» 

^^ 

— 

^ 

•  - 

— 

»^ 

M* 

-^ 

•~ 

r^. 

\ZL 

ci 

t> 

t.- 

•o 

C» 

^> 

r~ 

cc 

— 

ri 

t^ 

zz 

C": 

— 

"^i 

r; 

-r 

^-> 

^ 

^ 

^"^ 

— ;• 

cc 

— 

— 

C:; 

»-« 

tTt 

^ 

— 

ii; 

zz 

— 

— r 

•^ 

— 

'T- 

r»l 

^ 

ZZ 

tc 

c: 

5; 

"•    h  .-vi. 

'-~- 

— - 

^"^ 

*— 

^^ 

^^ 

«^ 

•^> 

^  t 

■r-  < 

---^ 

-  — 

-  -» 

H 

«». 

vM 

.  — ■ 

1^ 

^^ 

"* 

-  — _ 

1  -' 

-- 

_ 

— 

r; 

^; 

<--. 

~ 

-T- 

^- 

~^' 

— 

vr 

;C 

i^ 

— 

7.- 

— 

"-7 

z> 

t_- 

~^ 

-_2 

.3 

[  '^ 

i> 

— ~ 

^ 

2> 

C* 

C. 

^T 

^ 

■^ 

Z1 

j.^ 

^ 

z~. 

•.— 

3» 

-C 

fc^ 

r- 

~ 

-T" 

:c 

r  } 

t< 

■~  >  ! 

*->. 

;._  t  ^ 

•— • 

«->- 

«-^ 

— 7- 

zz 

— 

•^^ 

CO 

— 

T" 

cc 

— • 

-^ 

£^ 

^ 

c^ 

c^ 

^ 

ZZ 

;^ 

c; 

CT^ 

•  -  rf  •  — ^ 

cr. 

^ 

^ 

~ 

~ 

— 

— 

"— 

3* 

s* 

C'f 

f^ 

J^ 

r^ 

'^ 

^ 

"^ 

»c 

iC 

0 

0 

C^ 

f    ;^ 

— 

I 

1 

■    kJ 

_^ 

;7 

-^ 

— 

~r" 

~3~ 

r"; 

— 

"^ 

— 

-T- 

:i 

f^ 

i^ 

— 

"3i" 

— . 

zz 

^ 

— 

r- 

.^ 

i^   ■ 

'  __ 

-■  I 

~ 

LTt 

cc 

^ 

*^. 

— 

7^ 

7^ 

^ 

^ 

i."- 

J-» 

.."3 

~ 

c^ 

•^ 

c^ 

^ 

r^ 

'^ 

t^ 

_^ 

>— 

■^^ 

■^ 

-,— 

zz 

:;< 

\S- 

~ 

3» 

i~ 

€- 

^ 

— 

c^ 

^ 

;^ 

tr- 

C5 

Ci 

^^ 

,^ 

Z\ 

* 

-^ 

t^ 

^- 

— 

ir- 

•-« 

— r 

c^ 

— • 

■M- 

J> 

^ 

T^ 

t- 

^ 

r^ 

•^ 

^ 

S-* 

•^ 

cc 

»— 

5~. 

c; 

^ 

•^ 

^ 

..^ 

— 

— 

— 

©♦ 

G*  e< 

r: 

c^ 

r^ 

T 

T 

"TT 

T 

^ 

^^ 

i^ 

■^ 

!  -  • 

. 

-^ 

^^ 

T^ 

.-;; 

— 

~ 

— 

c^ 

7^ 

7-; 

^ 

^, 

i.~ 

^^ 

r- 

-^ 

t- 

zz 

C- 

rr 

^ 

■— • 

fr    " 

;    - 

t> 

i^ 

— 

-^ 

— ^ 

tr-/ 

£- 

^ 

~ 

t- 

C* 

*c 

»c 

*r^ 

c. 

z* 

yz 

JH 

^^ 

«?• 

c^ 

\  ^ 

i> 

It 

C;^ 

_i 

-^ 

Ci 

3-? 

t^ 

~ 

— 

1— • 

** 

cc 

^ 

—^ 

7^ 

-^ 

»^ 

i-C 

^ 

'.^ 

'^ 

t^ 

— 

t^ 

•^ 

Tr 

;-» 

^ 

~" 

t^ 

^ 

7^ 

t"- 

^ 

t'^ 

*^ 

ct. 

0< 

w^ 

cc 

"— • 

""  •  5^ 

C; 

~ 

^ 

O 

»— . 

— 

— 

t< 

"/ 

Zt 

Z". 

7"; 

'.'^ 

rr 

-T 

-r 

•T 

•-" 

•^ 

»c 

^ 

CO 

.- 

3y 

"3" 

— 

-^ 

— 

"3^. 

rt 

— 

•cr 

?■» 

JZ 

— • 

— 

,— 

c; 

^~ 

cc 

;7. 

CC 

-^ 

5/ 

'  -^ 

5 . 

T— 

r- 

^ 

— 

~ 

-^ 

£^ 

l> 

^ 

^ 

t^ 

r^ 

Zt 

i^ 

■^ 

t' 

~- 

cc 

zz 

ZC 

--O 

'■  ^ 

~ 

~ 

c^ 

-^ 

Zt 

c; 

c^ 

C* 

vC 

CO 

»• 

c^ 

i^ 

t^ 

cc 

^ 

•— 

3* 

■?• 

zz. 

c^ 

f^ 

t  ""■ 

— ~ 

■^ 

^ 

c^ 

r^ 

o 

nr 

r^ 

■^ 

r^ 

t^ 

^ 

c^ 

cc 

c: 

c^ 

C3 

c: 

<?> 

Ci 

CO 

■•■^ 

'H 

'd> 

^ 

;^ 

^ 

^ 

— 

— ™ 

■•— • 

o< 

(H 

c* 

r^ 

r^ 

c: 

c^ 

■»^ 

TT 

■^^ 

Ci 

»c 

kO 

CO 

.  '^ 

■  "■ 



~-r 

.-^ 

CC 

~ 

— 

_ 

f ' 

-^_ 

■^ 

_^ 

— 

i^ 

-; 

~z7 

— 

._ 

>* 

7^ 

rr 

4_r; 

z 

c^ 

~' 

•;  > 

^* 

Cx 

5'- 

r^ 

rt 

;- 

t'i 

:^ 

7^ 

Pi 

r^ 

z~. 

^ 

-r 

•^ 

rr 

•^ 

^r 

i^  '- 

'— • 

— • 

^-» 

— 

—— 

■•-• 

rr 

'— 

— • 

— ^ 

— 

— 

•— 

— 

— 

•— 

— 

— 

^ 

~~ 

~~ 

A  TABLE  OF  LOGARITHMS.  10.:5 


3^J  CO  O  G-}  C;  CO  t-- 

cr:  r^  CO 

CO  GJ 

-^  CO 

CO 

r^ 

,.., 

c;  '— 

CO 

CO 

— ~ — ^^  I 

2~<  :r;  Ci  C;  CO  »-::  O 

CO  >-0  rr 

G->  CO 

GJ  -r" 

»0; 

-r 

GJ 

1>  G^? 

UO 

uO  CO  1 

:^  Ci  CO  CO  -o  O  ';}' 

G<  O  CO 

CO  CO 

"  CO 

i-O 

Gi 

uO  G-( 

CO 

r*i 

^  CO  ' 

C5 

£^  Ci  G^  O  CO  T- 1  TT 

t-  O  G^ 

>.0  CO 

■"  c^ 

"O 

c?> 

t-^ 

-^  l- 

rr> 

o* 

lO  t^ 

-'_.  CO-  t>  t^  1>  CO  CO 

CO  o  c^ 

a   C75 

o  o 

o 

c 

1— ( 

1— < 

ft^ 

&<  G^ 

— ' 

G^ 

S^J 

O  T  CO'  Oi    ^    3-t    3-': 

CO  '-'  J> 

zz   tr- 

w  i-"^ 

CO 

cr. 

— 

T"  t-~ 

uO 

.- 

G-f  0< 

3sJ  i>  O  '-  O  t-  G  J 

iO  1>  'CO 

TT"  O 

L-O,  t-" 

CO 

!~- 

i-O 

—  lO 

CO 

cr: 

cr:  t- 

O  O  CC  >0  ^  Gi  --< 

c:  r-  o 

CO  '"' 

CO  o 

G< 

crs 

CO 

CO  cc 

lO 

l-H 

J>  CO 

,~^ 

"O  Ci  G^>  i-O  CO  '— 1  -^ 

t-  CC  GJ 

lO  CO 

O  CO 

CO 

CO 

cr: 

C^J 

Tf  £> 

--C  O  J>  £^  i>  CO  CO 

CO  CO  C5 

Cc  C'. 

c  c 

'^ 

■^ 

r— 1 

—1  r— 

1>1 

Cn* 

G^J  ©< 

1— H 

G< 

GJ 

O  O  '-I  iGJ  CO  o  c; 

T^  o  cc 

C5  G< 

f>  lO 

CO 

o 

CO 

CJ  'T 

CO 

CO 

GO  lO 

CO  CO  '-  G?  '—  CO  CO 

1>  CTj  CO 

CO  CO 

t^  o 

T— 1 

1-H 

CO 

"^  cr: 

rsf 

c^ 

ao  y-i 

•^  CO  CO  G)  —  C:  CO 

CO  -r  G» 

C'  CO 

iT-  C^ 

{^ 

CO 

O  CO 

^-> 

UO  ^ ! 

't- 

•O  C".  G-<  O  CO'  O  CO 

CO  cr.   G-) 

o  t- 

C  CO 

^^ 

CO 

1—1 

"— <  cG 

.-^ 

_ , 

•^  i> 

UO  O  l>  O  £^  CO  CO 

CO  CO  cr. 

Cj  CC' 

G< 

^ 

" 

e< 

G^  G^i 

-r  x;  :n  g*  o  c-.  i^o 

-^  O.  w 

G>  CO 

C^  'C^ 

CO' 

G) 

_ 

CO  C' 

— 

7-s 

-M      tS- 

i 

c":  CO  — 1  :o  G»  g:  ^o 

cr.'  ^  ^— 

cr:  o 

O  CO 

■rr' 

-* 

G? 

-  — 

,-^ 

f~~   CO 

'-<  O  C  cr;-  CO  w  ^0 

CO  G^  O 

L-  O 

c":  o 

r^ 

•—' 

1>  TT 

"^ 

") 

G^  CO 

-^ 

:;o  O  G-^  -^  i>  C  c^ti 

CO  c:;  GJ 

-^  t^ 

O  CO 

^ 

CO 

T— 1 

:o  CO 

cr: 

-t  CO 

"O  CO  !>  J>  {>  CO  CO 

CO  CO  c:; 

C:  Ti 

'^-^   o 

s-^' 

o 

1—1 

f^f 

G^  Gn« 

"-^ 

G^ 

G* 

c-0  G^  "O  —  "-j:  c-^  c 

CO  CO  o 

—  — 

ex  — 

»-0 

-~ 

*'  . 

C«  CO 

CO 

•^ 

uO  o 

CO  c:  G^  ■T'  CO  '-^  t-- 

O  G^  CO 

^  CO 

01   CO 

r- 

L^ 

uO 

»— »  CO 

c: 

OO  t^  t^  CO  O  T  G> 

^  CH)  J> 

»-0  G' 

•!-- 

'T^ 

CO 

UO  — < 

r- 

T^ 

'^  cc  ' 

»C 

i-O  CO  ■'-^  '^  t'~-  CG  CO 

CO  CO  '— ' 

T"  '^ 

O  G-J 

lO" 

CO 

^ 

CO 

T— 

"-^  CO  1 

-O  -vO  i>  i>  £>  CO  CO 

1— ( 

CO  CO  c; 

en  Cf 

G-( 

^ 

c 

•^ 

GJ 

G^  Ot   1 

s-j 

1 
I 

,-,  l-  TT  T— .  CC  CO  lO 

'O  1>  ^ 

l>  uo 

1-0  CO 

■^ 

— < 

r'^ 

C)  G^ 

r- 

-~. 

uO  G>  ' 

-:*■  cr,  CO  i-O  -r  G?  CO 

G*  -V  >-0 

c^  O 

o  CO 

.^ 

^ 

CO 

1-0  o 

f-. 

i,--. 

O  -^  ' 

'O  '^  •-*  CO  G<  ^  O 

CO  «D  rj^ 

G?  O 

t^  ^ 

G/ 

cc 

^o 

'^)  c^ 

»^ 

I—, 

i>  CO  1 

■^ 

o  CO  r»i  -r  i^  CO  G» 

O  CO  '- 

~c  c~ 

<Tj   G' 

lO 

^ 

CO  UO 

CO 

^_ 

90  CO  ! 

CO  CO  i>  t-  i>  CO  CO 

CO  CO'  CC 

CC  Oj 

cr.  O 

»— ' 

T—. 

T-< 

r^> 

G^  G-}  1 

1 

gI 

Z') 

I 

j   ^  CO  T-,  c  c:  tr.  o 

Gj  CO  '— 

C:  C: 

T—  :^ 

•-- 

-— « 

cr. 

CO  CO 

r^ 

r^ 

-^  i 

-T  C5  "^  CO  i-O  CO  C 

^  CO  J> 

>-0  g; 

CO  ^ 

CO 

CO' 

CO  CO 

\^ 

CC)  CO 

GJ  C<  T-H  O  Ci  CO  l^ 

-.  CO  »"' 

cc  t- 

TT  GJ 

CC' 

CO 

c^ 

CC  CO 

r^) 

~ 

"*  o 

ic 

-o  CO  -^  Tt  CO  cr.  G^ 

^:  CO  1-H 

CO  CO 

CV  G^ 

T^ 

1^ 

• — . 

G^<  ^ 

CO 

-— 

CO  CD 

CO  CO  1>  l>  J>  t>  CO 

T— 1 

CO  CO  Ci 

c:  c* 

Gs» 

^ 

" 

»-H 

■3 

<^(  ©* 

G<J 

-'~.  '•^ 


t-cococ:OGiLOcr:T}<©s'T-,.^,...^._^  ^—^^^w 

-j<  O  ■T'  CO  t^  ^t;  '— 1  uO  CO  CC  CO  uO  O  "^  "-0  -co;  ^O  G--f  f-^  ^^  c^  c^.  -^1 

cr:  cc  CO  j>  CO  »-0  -f  G-j  o  CO  CO  rf  G^(  c:  CO  CO  CD  i>  CO  O  CO  &5  CO 

-Tf  i>  O  CO  CO  cr.  Gi  UO  CO  O  CO  CO  cr;  —  'T'  t^  C  G-)  uo  CO  o  CO  u-> 

-o  CO  i>  t^  i>  i>  CO  CO  CO  cr:  c;  c:  c:  o  O  c:  i-i  ^  '-I  i-H  G^  ev(  ©:» 


C-  CO  O  CO  1— «  "^  c:  lo  CO  G'  C'G  CO  G'-i  CO  '^  CO  CO  'T^  c:  i^  O  CO  CO  I 

■O  I— '  O  i>  CO  CD  G'J  J>  C  I— I  CD  f^  CO  !>  cr;  crx  CO  uO  O  "^  J"^  r^  CO  I 

CO  CD  uO  -^  :0  0(  ^  ex  CO  CO'  -r  i-i  C:  CO  CO  O  {>  -^  ^  l^  .CO.  O  )0  I 

-^  t>  C;  CO  CO  C:  G^  -rr  i-  O  CO  CO  OO  —'  'T  L--  CC.  GNJ  uO  t-  O  OJ  o 

CO  CO  t-  L-  i>  L-  CO  CO  CO  c:  c:  o;  cr;  C  c;  C  C  r-,  T-,  ,-,  (^)  e)  G^  I 

-  G^  j 

G<  •      1 


-  '  t^  G-/  CO  »— '  t"  -^  ■r-\  T--  Gv  lO  C:  t>  1>  O  CD  UO  CO  -rr  ^T  CO  CO  c: 

uj  1-,  ;o  CO  cr:  t^ — ^  o-;  G^»  co  g*  c:  uo  c:  gj  G<  »-  co  "^  -co  cc  t-<  o 

COCOG<i-iOCr:COCO*~CO.^COOCO«OOiO!'-'CO'*--'I>CO 

T  i>  o  CO  CO  CO  ^  'TT  t^  O  CO  uo  CO  1—1  "^  CO  CJ;  o»  -^  i^  O  ©■»  lO 
■o>  CO  t^  i>  L-  t-  CO  CO  CO  C5  ci)  C5  cr;  O  O  O  O  ^  "  <-t  G-}  Gi  oj 

G? 


-  CD  t-  CO  c-  o  T-i  3-/  CO  ■:*>  lo  CO  r-  CO  cr;  c;'  '-I  G-i  : ;  -7-  UO  co  ••-  x  ' 

l^.  ^  rf  '^f  rp   iO  "O  UO  UO  UO   UO  ^  uO   i.-^   UO  CO  CO  '-     ■_    ■-   c-    CO   C"    CT  i 


1- 


}f4 


A  TABLE  OF  LO&ARITIIM. 


1 

i 

CO  o)  ^0 
^  -f  I- 

-1   t-  OJ 

o  c>j  o 

:o  C'O  CO 

3^f 

lO  o  O  CO  CO  CO  O  ^  cr^  CO  'T'  c<  i-^  cj  cji  t-'  G<  lO  o  o  ■ 
crs  o  C5  ^o  o^^  i^  —1  CO  CO  CO  '-"  c:  CO  t--  O  ej  CO  G'  o  t^  i 
t-  CO  i>  Oi  c-  —c  CO  O  -t*  CO  oj  o  C7)  3^  -o  c:>  3>  i^-:  CO  o  1 
I-  o  o^  "C  t-  o  GJ!  »-o  1--  a;  G<  r*<  CO  c^  —  CO  CO  CO  o  c--: 

CO   '^   -"^   ^   -^  O   O   lO   >0   O  CO    CO  CO  O  1>  1>   l^  t>  CO  CO 

CO'  :c  CO 
CO   CO  G^ 

':^  ot  a> 
^  :>i  lO 
>*  CO  CO 

-t:'  O   —   cr.   G!   G»  Ci  O  CO   -^   CO   CO   3-»   CO   1^   cip   G»   CO   BO   o:   ! 

■^  o  t-  r-  CO  CO  CO  ctj  GTi  Ci  i>  -^  O  -^  i^  cfj  o  c:>  t-  ^  i 

»-o  c;  o  o  '^  cni  CO  i^  '-  ^  o;  CO  t^  o  CO  cb  o  Gj  Lo  CO  I 

t>   O  G»   O   J>  C:i   G;   rj-    1--  C;   '-'   TT   CO  C5   T-,   CO   -O   CO   O  CN   j 
CO   ^    '^■'    -^   -^   T    O    O   ^   -0   CO   CO   CO    CO   i>   1--   t-   t^    CO   CO 

! 

CO 

2>    ^   O 
CO   C-'i   1-- 
■-0   OJ   t- 

3^   CO   CO 
3^ 

2( 

G-<    O   CO    G<    t-    t-~    iO   CO   CO   uO  CTi    Cr.^   t-   G^    ~   -^   G*    O    '^    GJ 
Ci  o  c^j  t^  CO  CO  e;  -^  1-0  ^:  CO  O  -o  r-.  -f  CO  t--co  >-C  Gi 
3-J   CO  G)   t>   G-<  CO   ■r-(   lO  O   CO   i>   '-'   -r  CO   T^   -■^'   r^   O  CO  CO 
t-  CD   G>   -:^"   t^  CTi  0-(   -^'   CC'  Ci  T-i   -^  CO   CO   I-"   C3)   »0   CD  O'  G^ 
CO   C3i   -^   -^   "*   -^   >-0   to   >0   ^0  CO  CO  CO  CO    i.^  1>   i>   t^  CO  CO 

to  O  t- 
3-»   t>  '-I 

Tf  ctj  1^0 

CT5   —  ^ 
>J  CO  c^ 

^5 

T-i   O    **    O   »-<  CO   '-<   CO   CO   CO   >—    C"    GJ    O    '-<    C^i   G^    OO  GO    O 

-f   ^   "^  G>   CTi   rr  CO   O  '— 1   1— 1   O   l^  CO   CO   — >  CO   '^  CO   G^   C:; 

o  lO  o  lO  c;  -?<  CO  CO  t-  r-i  ijr:  00  GJ  o  Ci  G»  >-o  CO  1^  c: 

l^   Ci    3J    -T    --O    Ci   T-   rr  O   CTi   !-<  CO  CO  OO   O   CO    O   t^   O   3-^ 
COCO'^"^'^'*Oi-0!^OCOCOCOCOL"^t-t^l>COCO 

1 

O  Tt  '^- 
t^  3-j  :o 

^   I-   G^ 
CO  '— '   ^ 
3n>   CO   CO 
GJ 

c.  en  »^  I-'  ur;  30  CO  -r  £-  t-  CO  -^  CO  rr  cr.  »—  — '  ^*.  '-.  c-2 
CO  o  Ci  t^  -^  cr-  CO  o  f.--  I-  CO  CO  Ci  '^r  i>  O  '-^  O  o  CO  1 

t-  GJ   l^   G»   t^  '-•  CO   O   '^  CO  GvJ  CO   Oi  CO   CO   O  CO   CO   CO  '-1  j 
COC?5'-^-?'COC2^-*COCOt-i.COOOOOCO'0    1>C:CJ| 
CO  Ci   '!i'   rr   '^   "^   O'lO   ^3)   lO   CO  O  CO  CO  I-   1>   I-   t^  l>   CO   ; 

t 

1 
j 

t 

CO  o  -< 

—,    £-    r-. 

CO   rf   O 
CO  1—1  Ti< 
3--f  CO  CO 

C5^J 

I-  cr.  CO  O  cr.:  -^  lo  3^  t-  l-  ^  c:;  —«  C'  CO  CO  '-'  O  t-  g-j  I 
CO  **  -^r  CO  c:  lO  cri  G-}  CO  CO  G-j  ex  CO  — '  T  t^  CO  CO  CO  '-."  f 
uoo>-0  0-J-c;coco3^coOcO{.-^"-tri-'Ocococrsi 

CO  ex   1— 1   Tf  CO   CO   ^   CO   CO   CO   >-<   GO    »^0  CO   O   G<    >-0    f^   c;    '— 
CO  CO  '^  ^  -^  -^  O  O  ^   O  CO  CO  CO   CD   J>  t-  l^   C-   L-   C3 

ct 

C--   lO  j> 

O  '-I   O 
■O   3}   i- 

CO   ■>— >  CO 
3^?  CO  CO 
3} 

3> 

•O   ex   1^   G>    G/  ex   — 1    O    "O    CO   i"-   G»    'C    O   CO    CO    O   "-^    Cj    t^.'  ♦ 

CO  ex  c^  CO  --0  o  o  CO  (X  c:  c:>  co  gj  t-  '-^  cO'  -c  '3  co  — '  j 
O)  v^  CJ  L^  G<  j^  »-i  o  c.  r;  tr-  t-"  "O  co  G{  >o  co  '—  -r  c- 

CO   00  1— 1  CO  O   CC  r- 1  CO   O  CO  O  CO   >0   O   O  G^   "^   t^  c:   i—     ■ 
CO  CO   ■^   -^  •^   -^  >-0  .O  UO   uO  CO  CO  CO  CO  l>  t-  l^  t^   l^  CO 

S.J 

o  3  o 

-r  C5  ^ 
CO   O  CO 
3^   CO  CO 
3^ 

CO  CO  CO  -^  CO  -^r  CO  CO  O  CO  cc  lo  o  '-<  O  CO  O  '-^  '-  CO 

C^   -^   "*   CO   O   CO   O   CO   O   >-0   -^   Gs»   Ci   -^  CO   O   G-»   Gi   '—   CO 
O   >-0    O   O    C    -^  ex   CO    t>   '— '    '-'^  ex   G-*   CO   C:   CO   O  (X   G}    -rr 

cocoi-'COcocoOco»OcoCGv{Oi>cxG<'^coc:'— 

CO  CO  -^  ■^  -^  "^   O   U3   O   >0  CO  CO  CO  CO  CO  t^  l^   t--   l^  CO 

- 

-^   "^  O 
'^  o  ^ 
— »   t-  <3» 
X   O  CO 

"^^^  CO  CO 

^    1--   ex  CO  <X  O    ^  CD   -:f   CO   O  CO   -r^  O  CO    -*   C^    G.'    G-*    '-' 
GO  C;   O^   CO   >-0   T-t  CD   C^   '— '   '— 1   '—'  CO    O    O   "^    1~^  CO  <X  CO   CO 
t>  O)   l^   G->   l~-  G-J   CO   O    '0  ex  CO  CO   O   -^  t^   O  CO   CO'  Ci   Q> 
lT-  CO   O  C^   "-O  CO   O  CO   '-0   l>  O  G^   »0  J>  CJ   G^f   -^  CO   CO   '-1 
COCO-^'^'^'yOUD^uOCOCOCOCOCOt-i^t-C-CO 

o 

j 

<-  '-:  CO 
CO  -r  C5 

CO   r*  Cj 
O    O   G» 

-yi  CO  CO 

COCOCXCSCOCOOCOCOCX'-'   —   COG.»COG^COG-'T*CO 
3s^   ..-i   —  C*:;   '— 1   r--   G->   LO  l>   C~   t^   O  T-(   {->-  r-c   rt   '"    CO   »-0  C3 

o  O  »-0  O  k-o  o:  ♦*  OO  c<  CO  o  "Tf  CO  '-'  »o  CO  "  •*  t^  O 

O  C^   O  CO   O   l-  O  CN<   »-0  l-*  C>  G>  "t"  l>   C5   ^-<   -^  CO  CO  '— ' 
C0C0"^'^'^'^>^>^^'2>^<ii3OC0C0C0t^C*t-l^C0 

u 

3  .  -  ir- 

-VI   --    -rf   ^.-;   "o   L^   CO   -X   O  —   3J   CO   •--"   'O   C3   t-   CO  C"    C    '— '  ( 

?-  i-l  t^  {.-  t-  i^  L-  r-  c:  CO  CO  cc  :.-.  c:  co  co  co  cc  c.  as  , 

105 

A  TRAVERSE  TABLE,  OR 

DIFFERENCE  OF    LATITUDE  AND  DEPARTURE, 

When  1  minute  is  calculated  to  5  minutes,  and  from 
thence  to  10,  15,  20  and  so  on  to  60  minutes  or  one  de- 
gree ;  and  from  1  degree  to  1  degree  and  30  minutes,  and 
to  2  degres,  and  so  on  to  90  degrees  :  and  any  distance 
from  1  to  9  poles  or  chains,  by  which  it  may  be  understood 
to  extend  from  10  to  90,  or  from  100  to  900,  or  from  1000 
to  9000,  or  from  10000  to  90000,  observing  to  move  the 
separatrix  one  or  more  places  to  the  right  band,  as  the 
number  of  cyphers  on  the  right  of  the  integral  distance  will 
denote,  and  the  rest  will  be  decimals,the  two  first  of  which, 
on  the  hand,  may  at  all  times  be  culled  links,  when  the 
distance  is  given  in  chains  and  links. 

JS'ote.  Difference  of  Latitude  is  called  Northing  and 
Southing.  Departure,  Meridian  Disrance,  or  Longitude  are 
the  same  as  Easting  and  Westing. 

To  find  the  Latitude  aad  Departure^  for  any  Course  and 
Distance. 

If  the  Course  be  more  than  45°  look  for  it  in  the  column 
marked  Latitude  ;  if  lesrthan  45°  look  for  it  in  the  column 
marked  Departure  ;  and  look  for  the  Distance  at  the  "righ 
or  left  hand  columns  :  against  the  Distance,  and  directly 
under  the  Course,  stand  the  Latitude,  or  Northing,  he.  in 
whole  numbers  and  decimals. 

If  the  Course  be  less  than  45°,  the  Northing  and  South- 
ing, will  be  greater  than  the  Departure,  or  Easting  and 
Westing,  but  if  more  than  45°,  the  Easting  and  Westing 
will  be  the   greatest. 

When  the  Distance  exceeds  9,  90,  or  900,  &lc.  it  will 
be  a  Multiple  of  some  numbers,  from  1  to  9,  or  from  10  to 
90,  k.c.  Suppose  the  Distance  to  be  16,  which  is  a  Multi- 
ple of  8  :  double  the  numbers  found  against  8,  in  both  Lat- 
itude and  Departure,  and  you  will  have  the  respective  re- 
sults :  for  example  ;  suppose  the  Course  13®  30/,  and  the 
Distance  16  Chains.  Under  13^^  30',  we  find  under  Lati- 
tude, 7,778664  ;  this  multiplied  by  2,  gives  15,557328.  for 
the  Dep,:rt:rc  :  against  8  we  find  1367488,  which  mvltipli- 
ed  by  2  gives  3,734976,  which  is  the  answer,  for  16.  If  the 


lOG  OF  A  TRAFERS  TABLLl. 

Distance  he  17,  to  the  number  before  found  t'br  IG,  add  the 
number  against  1  :  or  lor  19,  double  the  number  against  9, 
to  =vhich  add  the  number  ::gainst  1  ;  and  for  20,  look  a- 
gainst  2,  and  remove  the  separatrix  one  phice  to  the  right 
hand,  and  so  for  30,  40,  50,  60,  &c. 

Suppose  the  Coarse  N.  27°  30'  E.  and  Distance  from  3 
to  SOOOO. 


Latitude. 

Departure. 

3 

2,660931 

3 

1,335193 

30 

26,60931 

30 

13,85193 

300 

266,0931 

300 

138,5193 

3000 

2660,931 

3000 

1385,193 

;oooo 

26609,31 

30000 

13851,93 

The  above  Distance  may  be  called  Chains,  and  then  the 
TWO  figures  of  decim^ils,  next  to  the  separatrix,  will  be 
Links  or  decimals  of  a  Chain. 

Again,  suppose  the  Course  22*',  and  the  Distance  70 
Chains.  Against  7,  the  Latitude  will  be  6,490  ;  or  call  it 
70,  and  then  remove  the  point,  one  place  to  the  right  : — 
thus,  64,90,  and  so  of  Departure  ;  2,622,  altered,  makes 
26,22  Links,  <S:c. 

Suppose  t"he  Cour?e  as  above,  and  the  Distance  70  Links 
more  than  the  respective  Distance.  Look  against  7,  rmd 
remove  the  separatrix  one  place  to  the  left  hind,  and  then 
the  two  decimals  will  be  Links  ;  as  against  7  you  will  find 
6,208,  altered,  will  be  62,08=to  62  Links,  and  so  of  any 
other  number  of  Links,  as  they  are  governed  by  the  same 
laws  as  whole  numbers. 


A  TRAFERS  TABLE. 


107 


\A 


D:st. 

DeL'artufe  .•  ;  -ariire. 
jy       2' 

I     , 

L-.  000291  O.UOOoc-- 

o 

0  000582  0.001164 

3 

0.000373  0.001746 

4  ' 

0.001164  0.002328 

6 

0  001455  0.002910 

6 

0.001746  0.003/' ..2 

.  7 

G.C02037  0  004074 

8 

0  002328  O.0G4656 

9 

'  002619  0.005238 

5'      10' 

X 

w  00  iij4  0.0(^2509 

2 

0  002908  0  0058 18 

3 

0  004362  0  0'.)8727 

.4 

0  005816  6!  011636 

5 

0  007270  0  0!4545 

6 

0  008724  0  017454 

7 

:•  010178  0  0203G3 

8 

:•  011632  0  023272 

■■' 

.'  013080  0  026  U'l 

2.:.'  ,    30' 

1 

.:  007272  0.0(£726 

2 

^  014544  0  017452 

3 

':  r,21816'i  026178 

4 

•  ■.  ".^9088  0  034904 

5 

0363G0O  043G30 

6 

043632  0  052356 

•  7 

■  050504 u  061082 

8 

'^•58176  0  On?808 

9 

<G5448  0  07  8534 

4''   !   50' 

!•  ui3089  0.014543 

0  036178!6  02':^086 

0  039267;0  043629 

4 

..  052356  0  058172 

^ 

•^  Ur:5U5  0  072715 

G 

1  078524;0  087258 

7 

0  09 16  23  0  101801 

8 

■■■■   K>  1722  0  lh;344 

9  1 

0  117801,0  138870 

I    Departure. 
3/ 


jDeuartiire 
4'     ■ 


Dist. 


tJU0087  3.0. 
0  001746jO. 
0  00261910 
0.003492.0, 
0.004365|o. 
0. 00553810. 
0.0061 11 'o. 
0.00G994|0. 
0  00785710, 


0'>^1164 
002328 
0034. 2 
004 G56 
005820 
006984 
008148 
009312 
01G476 


0,0c;433G;0. 
0  00867210 
0  013008 jo 
0  01'^34a!o 

0  0216^0:0 

0  02f^016'o 


(MJ5ci7! 
0116341 
0174511 
0232G8i 
029085i 
0349021 
040719! 


0  03o352lO 

0  03468810  046536 

0  03 9024 ie  ('5^353 

3.''  ;   4oT~ 


0.010170:0. 
0  020340i0 
0  0305  ]0j0 
0  040680iO 
0  0-X?850!0 
0  0 '10^0,0 
OvJ7n90  0 
0  081360  0 
0  0915.30  0 


0  \»  15'.  97 
0  031i»94 
»;  047  i;l 
0  063.  88 
0  679  985 
0  0'-5P82 
0  111979 
0  ^  -  T6 
0  1439731 


011-^5 
023270 
034905^ 
045540; 
0587751 
071^810; 
OP  1445 
093080! 
104715' 


1C5 


A  TREVERSE  TABLE. 


0o23o0 


1047 1  i> 


9   ^;  £>?':c32  0  157068 


0  - 

^'  i   -  ;  -  ■  -  ■ 

2  99385 1  jo  0785:3  3  , 

**  o 

5  997702[0  1570501  e 

C  -  -  ,  ....  ^ 

7      .  8 

S  9965t'5iO  e;?oo74;  9  j 

2«>  SO'  i     \ 


£7"  30' 


17   1 


I 


■  H  \-  j'  3  c.              4 

;  5  .           .  ;  i  4  99'          '5 

6  roi  6 

7  '^^  ■-  ^  -.-X,- J  .7 

8  :7&192  [  8 
i  9  i  b  9V8632  0  3 1 40  >  1  |  o  ^^\  GsOJ u  3;^ .  o 53  '  9 

'  '"              '    3*^       "  i'  ♦fco^  3o'  j   3"  -:^  ' 


t>7- 


.053330 


1      1  .0.9--^ 

'      2  flP' 

j     5  J4  993I'>00  26?t>J0 

^    7  u  ^ai-i..  -  -----^ 

8  7  99K»40'^:J  4I86S8 

9  8  V        ■        4710?4     It     J: 


0  \^9£097  0.1 


1 


104672  :  096194  0  ie20S2t     2 

4  9?0485i0  30523' 


P.     i 


:    r 


,  1         .  4;0.0€9756     ['     ^- 

1  2  (l  9951280  13951?     | 

I  3  ':  -:-       -  --    j:    .: 

!  ^  H^ 

;  7 

8  • 

*  9  t)  -_  iOi-'7o   ^  v_i"v4 


T— T~! 


4*^  3C»' 


OTR4  5':        I 


j,     5  9ol,7^    •  -^,^^'^-- 
\     0  9c  8 !  5  3 '  '^  549 1 9?f 


:1  TRAVERSE  TABLE. 


109 


Latitude, 
o -o 


Departure, 


Latitude,  iDepartuie 


0. 99G 195  0. 087 15tJ 

1  992390jO  171312 

2  98C590p  261468 

3  985780  0  348624 

4  980980;0  435780 

5  9771G0J0  522936 

6  9743'>o!o  610092 

7  9715G0!o  €97248 

8  966760*0  784404 


840 


6o 


0.994522,0.104528 

1  989044|0  209056 

2  983566'0  314004 

3  978088  0  418112 

4  9726100  523140 

5  967132  0  628168 

6  961654;0  732196 

7  9561 76*0  836224 

8  950698  0  941252 


8  30 


0.992546:0.121869 

1  985092|0  243738 

2  977598|0  365607 
13  970184|o  487476 

4  952650|0  609345 

5  9551960  731214 

6  94870210  853083 

7  940368^0  974952 

8  922754!  1  096821 


0.090268,0.139173 

1  980536 0  278346 

2  970804;o  417519 

3  961072|0  55::692 

4  951340|0  6958G5 

5  94 1 60810  835038 

6  93I876|o  974311 

7  9221 44;  1  113334 

8  912412'!  252557 


84°  30' 


0.99535,' 

1  J99071C 

2  986074 

981432- 
98679C 
972148 
977506 

962864 


0' 


0.0951-42 
0  191684 
0  287526 
0  383368 
0  479210 
0  575052 
0  670894 
0  766736 


968222  0  862578 


830  30'   6°  30' 


0.99353410. 

1  987068|0 

2  980602  0 

3  974136J0 

4  967670;0 

5  961204,0 

6  954738i0 

7  948272!o 

8  94I8O6I1 


113198 
226396 
339594 
452792 
565990 
670198 
792386 
iJOooo  4 
018782 


820  .30' 


30' 


0.9914070. 

1  982814'0 

2  97422110 

3  96562b!o 

4  95703510 

5  948442:0 

6  939849'0 

7  9312S6|l 

8  931663  1 


130521 
26 1045 
391563 
522084 
652605 
793126 
913647 
044168 
174689 


81*^  30' 


8°  30' 


0.98897810. 

1  977956!o 

2  9669.34:0 
955912  0 
94489olo 
9338680 
922846  1 
91182411 


8  900802(1 


147803 
295606 
443409 
591212 
739015 
886813 
034621 
182424 
330227 


Dist. 


liO 


J  TIUFKRSF 


i.r>L.r^ 


A I :ure. 
90 


!i  975?76;0  312868 
|2  963064[0  46^302 

3  9507520  625736 

4  934440!!  >  7G2170 

5  9:261  23 

6  913816* 


0  93G604 

1  09iOc8 
7  901504l1  251472 


Lai. 


Lude.    Deuart.irJ 
30'   !    9'    31.' 


i8  88919211  4079U6 


O.i8b248  0.16cO41 

1  972596  0  3300b2i 

2  9588440  495123! 

3  9441   0  660164^ 

4  931440  8252051 

5  9I7bSoO  990246f 

6  90303611  1552871 

7  888384  1  320328! 

8  8 76632!  1  48536y 


D-t. 
1 

3 
4 
5 
6 
7 
8 

Q 


1 

2 
3 
4 
5 
6 
7 
8 
9 


|i?.9£>480C'0.173b48 
(1  ^696 lejo  357296 
|2  954424|0  520944 
3  93-232jO  694592 
1  924040;n  868240 
\n  90884G|1  041888 

16  893656J1  215536 

17  878464(1  38i>i84 
ia  863272^1  5^2832 


0.983i;17!0.l82229  i 

1  966434b  S64458i  2 

2  9496510  546G87  3 

3  9328680  728916:  4 

4  916085|0  911145,  5 

5  8  99302 'l  09337  4  i  6 

6  882519  1  275603  7 

7  865736  1  457832  8 

8  848953  1  640061 


1  [0.981627  O.hjObiO 

2  1  96S254  0  381620 

3  12  954881^0  572430. 

4  b  926508|0  763240 

5  1 1  90b  13510  954050 
a  f5  889762  1  144860 

7  16  0713891  335670 

8  \l  85301  n;i  526480 

9  !8  8316431  7172^^0 


78' 


12° 


1  0.97^148  0.207912 

2  M  95629610  415824 

3  5J  934*44  0  623736 

4  3  912592'0  83]648 

5  4  890740  1  0395. >0 

6  [5  86883'  1  2474-^2 

7  h  84703f-il  455386 

8  (7  8251 84!  1  663296 

9  -8  803332'!  ^71208 


0.979881 

1  959774 

2  939661 

3  919548 

4  899435. 

5  8793221 

6  359209 

7  83909ei 

8  818983! 


0.199.361 
0  398722 
0  598083 
0  797444; 

0  996805| 

1  196166 
1  395527 
1  594888; 
1  794249 


77'  30'   12*^  30' 


0.976259 
1  952418: 
928677i 
94)4836; 
881095| 
8.57354i 
8335131 
809672 
'-8r.331 


0.216431 
0  43286 2j 
0  C49293: 

0  865724 

1  082155 
1  298.586; 
1  5150171 
1  731448' 
1  947879! 


i 

<± 

3 
4 
6 
6 
7 
8 

Q 


.i  TlUyERSE  TABL 


Hi 


Latitude,  j  f'epar.uie. 

Lt^.txiiide.  L'epurtuifc. 

iy.<. 

7  7^  i  i;;^ 

j   7i.°  30'  ;  13"  30' 

Di'-t. 

i 

0.5J7437U'0.2'ii4^oi 

i  0.972333  0.233436 

1 

o 

1  948740  0 44S901 

1  944666:0  466872 

Q 

;2  923110  0  674853 

2  9169990  700308 

3 

4 

3  897480^0  899804 

•3  889332:0  933744 

4 

5 

i4  8718oO!l  124755 

4  ^CAdijbn   K7180 

5 

6 

J5  846220il  34970G 

!  5  8339[<jil  400616 

6 

7 

'6  820590J1  574 G57 

6  806331!  1  631052 

7 

o 
o 

7  7959G0i"l  799608 

1  7  778664'!  867488 

o 
o 

9 

8  76033C 

76" 

i 

):2  024559 

1  8  750997 

i2  100924 

9 

i 

i-  I'i'' 

;  75  30' 

14e  30' 

1 

0.97U296  0.241 922 

0.968111 

0.250370 

j   1 

2 

1  940592;0  483844 

1  936222 

;0  500740 

o 

3 

2  91G888J0  725766 

2  904333 

0  751110 

3 

4 

3  88118410  967688 

3  87244-1 

:1  001480 

4 

5 

1  851 480;  1  209610 

4  840555:1  251850 

^  i 

0" 

5  82177611  451532 

5  808666  1  502220 

6  ! 

7 

6  792072:1  693454 

6  776777  1  752590 

^  1 

0 

7  7623684  935376 

7  744888  2  002960 

8 

D 

0  732664*2  177298 

8  712999:2  253330 

9 

75«      15^ 

i   74^  30' 

15..  30' 

; 

1 

3.965926  0.258819 

0.96359410.267228 

1   i 

o 

1  931852 

jO  517638 

1  9371 88jO  534556 

o      i 

~    1 

:3 

i  897778 

,0  776457 

2  900782  0  801784 

3  i 

4 

3  863701 

!l  035276  ; 

i  3  874376  1  069112 

^ 

O   i 

t  839630 

1  394495  1 

1  4  837970  1  336340 

6 

(3   ! 

5  795556 

'l  552914 

1  5  801564il  603578 

6 

7 

)  761482 

1811 733 

6  7751 58ii  870896 

7 

8 

7  727408 

2  070552  1 

7  748752}  2  138224 

8 

p  : 

3  703334 
74^ 

2  .329371   1 

,  8  712346 

2  405452, 

9 

1 

16     i 

73°  30' 

\C/^   30' i 

t 

1  i 

f.9.126^  0.275637 

0,958783 

O.L'84O04 

1 

2  ; 

1  922524  0  551274 

I  917566 

0  568008 

2 

3 

-^  883786i0  826911   : 

2  876349 

0  852012 

3  I 

4   1 

>  815018 

I  102518  i 

3  835132 

1  136016 

4 

5  ' 

1  8063101 

1  378185  II 

4  793915' 

1  42002C 

5  1 

6  i 

5  767572' 

1  653822   j 

5  752698  1  7040241 

6 

7   i 

.5  72-J834i 

1  92.0459  j! 

6  711481  1  988028 

7 

8  j 

7  690096 

2  205096   ii 

7  670264' 2  272032 

8   ' 

9   ! 

^  651358 

2  ^80733  '\ 

8  629047!^  55603G 

9 

ili 


A  TRAVELSE  TABLE. 


Dist. 


LatitU'lc. 
730 


Departure. 
17 


Latiiucle. 
72  30' 


lUej'arture. 
17o  30' 


0.956305! 

1  012610! 

2  078915 

3  825220: 


!0. 292372 
,0  504744 

0  .S771 16 

1  1G9488 
|1  781 525' 1  461860 
|5  737830' 1  754232 

6  693135  .2  046604 

7  650440:2  338976 
18  6067452  631348 


Df?t. 


0.9536810.300694 

1  90736210  601388^ 

2  06  J 043:0  902082 

3  C14721il  202776 

4  768405|l  503470 

5  72208611  804164 

6  675767)2  104858" 
.7  62944812  405552 
8  583]  29*2  706246 


|0. 951057(0 
.'1  902114:0 
2  85317 1|0 
13  804228|1 
|4  755285  1 
5  706342;  1 
16  657399  2 
7  60845612 
iS  559513^2 


/I 


1  o 


1   0.945519,0, 


891038!0 
8365570 
782076jl 
727595]l 
673114,1 
610733,2 
7  564142|2 
^   ^-^^9671 '2 


OUi 


309017 
618034 
927051 
236068 
545085 
054102 
163119 
472136 
781153 
190 

325560" 

651136 

976704 

302272 

G27940 

953] 08 

278976 

604544 

930212 


0.948288 


70' 


10.939693 
1  879386 


20*^' 


3   2  819079  1 


3  758772|1 

4  69846511 

5  63815812 
^  57705112 

7  51754^2 

8  457C2  /)3 


342020 
684040 
026060 
368080 
710100 
052120 
394140 
738160 
078 'j  80 


896576 
834864 
793l52j 
741440; 
6897201 
638016', 
586304! 


i!     8  534392 


0.317292[ 
0  634584 

0  951876 

1  269168 
1  586460 

1  903752! 

2  221044' 
2  538328 
2  855628 


700  30'  1  19*^30' 


0.942606:0 

1  8832 12|0 

2  827818,1 

3  7704241 1 


4  713030 

5  655636 

6  698242|2 

7  540848  2 

8  483454  3 


.333794 
667580 
001302 
335176 
668970 
002764 
336558 
670352 
004116 


I   6 90  30'  200  .30' 


0.936636  0 

1  073272  0 

2  80990811 

3  74754411 

4  603180  1 

5  61981(;i2 
G  557452,2 
7  495C88'2 
0  '13072-J  3 


350194 
700388 
050582 
400776 
750970 
100164 


451 350  i 
801552 
1517461  9 


A  TRAVERSE  TABLE, 


lli 


1 

o 

o 
O 

4 
5 
(\ 

7 


Latiindc, 

60^ 


Depurtuie. 


jC*.yoJ.3£();U.o583G8      | 

1  8G7IG{J|0  716736  | 

2  000740!  1  075104  | 


3  734320  1 

i  G67900  1 

!5  GO14G0  '^ 

G  5350G0  -^ 

7  40 r^' -ID  9 

8  4  C  22:0 


G 


701810 
1 50208 
50867G 
867144 
225412 
22o 


Ig 

!8 


.02718410 
854368'U 
781552:1 
70873G:1 
Co  3920.;  1 
5G31042 
490288:2 
41747212 
344G5Gi3 
G7y 


.374G07 
749214 
123821 
498428 
873035 
247G44 
622249 
99785G 
3714G3 
"23^ 


.920505.0 
841010|0 
761515|l 
G82020  1 
60272511 
523030  2 
442535  2 
364040  3 
284745  3 


GG' 


.390731 
78 1 462 
172193 
5G2924 
953655 
34438G 
735117' 
125940 
516579 
"24^ 


.913545  0 
827090  0 
740635,1 
6541 80!  1 


1 

2 

3 

4  567725  2 


481370:2 
39481512 
30836013 
22190513 


406737 
813474 
220211 
626948 
033685 
440422 
847179 
253896 
GG0633 


680  30. 


0  930382 

1  860764 

2  791146 

3  721528 

4  651910 

5  582292 

6  512674 

7  443056 

8  373438 


Departure 

21-. 30 


670  30/ 


0.923844 

1  847688 

2  771532 

3  695376 

4  621220 

5  543084 

6  466908 

7  390752 

8  316596 


0.3Go48~« 

0  73297'-: 

1  099461 
1  4C5948 

1  832435 

2  198922 
2  5G540n 

2  931 896 

3  298383 
22^-  30'' 


66Q  30' 


0.917025 


0.382G69 

1 

0  765338 

0 

1  148007 

3 

1  530676 

4 

1  912445 

5 

2  296014 

6 

2  678683 

7 

3  061352 

8 

3  444121 

9 

230  30' 


1  834050 

2  751075 

3  668100 

4  .'85125, 

5  5C2150J2 

6  419175  2 

7  336 20c  3 

8  253225j3 
65""30' 


.3:)8734 
797468 
196202 
594936 
993670 
392404 
792138 
189872 
589606 


0.909926 

1  819852 

2  729778 

3  639704 

4  54.9630 

5  45955G 

6  369482 

7  279408 

8  189324 


240  3C' 


.414677 
829354 
244031 
658708 
073385 
488062 
803739 
317416 
732093 


Dis'. 


1 

2 

3 
4 
5 

G 
7 
8 
9 


jy 


]1 


A  TRMTRSE  TABLE ^  - 


Di-t. 


LiiiUtULte. 
600 


9063080, 
8]261G'0 
71 8924]  1 
625x132  1 
531540j2 
43T84ai2 
344i5Gj2 
2504643 
156772  3 


422f3ia 
845236 
267854 
GD0472 
113090 
535708 
958316 
380924 
803562 


640 


26° 


jv).89879d'0, 
1  797596jO 
12  696394il 
|3  695192/1 
|i  493990I2 
5  392788J2 
io  291586  3 
i7  190384/3 
'8  088182  3 


6  3^ 


438371 
S76742 
315113 
753484 
191855 
630226 
068597 
506968 
945339 


0.891007  0. 

1  732014J0 

2  673021 

3  504028 
:4  455035 

5  346042J2 

6  23704913 

7  128056  3 

8  019063  4 


453990 
907980 
361970 
8 1 5960 
269950 
723940 
177930 
631920 
085910 


G20 


0.882948i0. 

1  765896}0 

2  648844J1 

3  53179211 

4  424740;2 

5  297688(2 

6  18063613 

7  063544 
7  946532 


640  30' 


lU, 


?parmre. 
25  30' 


28^^ 
469472 
938944 
408416 
877888 
347360 
8 1 6832 
236304 
755776 
225248 


0.9u255];0 

1  805102  0 

2  707653  1 

3  610204  1 

4  512755(2 
6  415306i2 
6  3178S^'^ 


7  220408 

8  122959 


430494 
860988 
2S1482 
721976 
152470 
582964 
014458 
443952 
874446 


l>ist. 


!i       630  30'       26  30'  I 


0.894901  0, 

1  789802|0 

2  684703|1 

3  579G04|l 

4  47450512 

5  36940612 

6  264307j3 

7  159208  3 

8  04410914 


4461o] 
892362 
338513 
784724 
230905 
677036 
123267 
569443 
015629 


62C'30' 


0.886977 

1  773954 

2  660931 

3  547908 

4  434C85  2 

5  32186212 


461731 
923462 
385193 
846924 
308655 
770386 
6  20883213  232117 
i|  7  09581613  693848 
!   7  ::8 279314  155589 


27  30' 


61^  30'  I  28  30' 

0878784  jo. 

1  757568!o 

2  636352!  1 

3  51513611 
4 
5 
6 


393920)2 
272704i2 
1514863 
03027213 
909056 1 4 


477141 
95428'^ 
431423 
908564 
385705 
862846 
339987 
817133 
294269 


i  i 


!  1 


A  TRAVERSE  TABLE. 


llw 


Liilitude. 

Departure. 

■   Lulilude. 

Departure. 

Dist. 

0.874G20 

29o 

eo'^  30' 

0.870322 

29«  30' 

D.St. 
1 

1 

0.484810 

0.4^2405 

2 

1  749240  0  9i39620 

1  740644 

0  984810 

Q 

o 

2  6238G0  1  454430 

2  610966 

1  477215 

3 

4 

3  49848011  939240 

3  481288 

1  969620 

4 

5 

4  373100  2  424050 

4  351610 

2  462025 

5 

G 

5  247720 

2  908860 

5  221932 

2  954430 

6 

7 

6  122340 

3  393G70 

6  092254 

3  446835 

7  . 

o 
o 

G  996960 

3  878480 

6  97257G 

3  939240 

8 

9 

7  871580 
60^ 

4  363290 
30^    i 

7  032898 

4  431645 
30^  30' 

9 

590  30' 

1 

0.8G6025 

=0.500000 

0.861596 

0.507519 

1 

2 

1  732050  1  000000 

I  723192 

1  015038 

0 

2  698075  1  500000 

2  584788 

1  522557 

3 

4 

3  4G4 100,2  000000 
-1  3301 2  rf  500000 

i  3  446384 

2  03007 G 

4 

5 

4  327980 

2  537595 

5 

G 

5  1981503  000000 

5  169576 

3  045114 

6 

7 

G  0G2175  3  500000 

6  031172 

3  552633 

■7  i 

o 
o 

G  928200  4  000000 

j  0  892768 

4  0G0152 

8 

9 

7  79-1225 

4  500000 

j  7  754364 

4  567671 
31o  3a' 

9 

1 
1 

59° 

310 

58'-^  30' 

1 

0.857167  0.515038   | 

■'     0.852607 

0.5224  78 

1    i 

2 

i  714334 

1  030076 

i   1  705214 

1  044956 

2 

o 
O 

2  571501 

1  556114 

2  557821 

1  567434 

3 

4 

3  4286G8 

^2  06^0 152 

3  410428 

2  089912 

4 

5 

4  285835  2  515190 

1  4  263035 

2  612390 

5  ! 

6 

5  143002  3  090228 

1  5  115642 

3  134868 

6  1 

7 

6  0001G9  3  6032G6 

1  5  968249 

3  657346 

7 

8 

6  857336  4  120304 

6  820850 

4  179824 

8 

9 

7  714503 
58'"^ 

4  635342 

7  673463 

4  702302 

9 

i 

32*^ 

^70  30' 
0.843359 

32^  30' 

1 

0.848048  0.529919 

0.537279 

1  \ 

2 

1  696096 

I  059838 

1  686718 

1  074558 

2 

3 

2  544144 

1  589757 

2  530077 

1  612837 

0 

4 

3  392192 

2  119676 

3  373436 

2  149116 

4 

5 

4  240240 

2  649595 

4  216795 

2  687395 

5 

6 

5  088208 

3  179514 

5  060154 

3  225674 

G 

7 

5  936336 

3  709433 

5  903513 

3  761953 

7 

i  8 

6  784384 

4  239352 

6  746872 

4  298232 

8 

,  9 

7  632432,14  769271 

7  590231 

4  83n5 j 1 

9 

\16 


A  TRAVERSE  TABLE. 


Latittule.  j  Departure.  ; 

r   Lrtitiule.  ; 

Departure. 

\   DM. 

1   1 

57"  1   :3;3<5    1 

56°  30'  ! 

33 J  30' 

Dist. 

0.}]38(J71;0.54k^:39   j 

0.833«54;0,551916 

1 

o 

1  C77.>i2:l  OS 9  2 78  i 

1  CG7708:1  103832 

2 

2  516uJ3i  633917 

2  0015G2'l  655748 

0 

4 

3  3oJG84'2  nshoG 

3  335416i2  207664 

4 

5 

4  193355  2  723195 

4  169270;2  759580 

5 

1  <3 

5  03202G  .3  207834 

5  003124^ 

3  311496 

G 

7 

5  870G97;3  81247o 

5  836978 

3  863412 

I 

0 

G  700368U  357112 

6  670832 

4  415328 

s 

9 

7  548039!  I  901751   ! 

7  504686 

4  967244 

9 

,'  -  * 

34'' 
0.559193   I 

55^^  30' 

34<^  30' 
0.566384 

1 

0.829038 

0.824145 

1 

I) 

1  G5807G 

1  11 8386  1 

1  648290 

2  472435 

1  132768 

0 

1  3 

2  587114 

1  677579 

1  699152 

3 

4 

3  31G152 

2  236772 

3  296580 

2  265536 

4 

5 

4  145190;2  7959G5 

4  120725 

2  831920 

5 

!  G 

5  971228;3  355158 

,  4  944  870 

3  398  304 

G 

i  7 

5  8032GG'3  911351 

.  5  769015 

3  9G4688 

7 

1  8 

G  G32304i4  473541  ! 

i  G  593160 

4  531072 

8 

;   ^ 

7  461312 
55'^ 

5  032737  1 

!  7  417305 
1   54  <^  30' 
i   0.814084 

5  097456 

9 

i 

350    i 

35'^  30' 

1  1 

0.819152 

0.573576 

0.580630 

1 

!  2 

I  638304 

1  147152 

1   1  628168 

1  161260 

0 

3 

2  45745G 

1  720728 

!  2  442252 

1  741890 

3 

4 

3  27G608 

2  294304 

i  3  256336 

2  322520 

4- 

4  095760 

2  867980 

4  070420  2  903150 
4  884504 0  483780 

5 

1  ^ 

4  914912, 

3  441 45G 

() 

7 

5  734064,4  015032 

'  5  698588 

4  064410 

t 

0 

G  5532  Hi 

4  588608 

i  6  512672 

4  645040 

8 

<^ 

7  372368 

54^ 

5  162084 

;   7  326756 

;5  225670 
36-^  30' 

9 

1 

36'^ 

i   53^  30' 
0.803826 

i  1 

0.809017 

0.5877  85 

0.594800 

1 

1  2 

1  G 18034 

1  175570 

1   1  607652 

1  189600 

.1 

3 

2  427051 

1  763365 

1  2  41147S 
:  3  215304 

il  784400 

3 

4 

3  236068 

2  351140 

2  379200 

4 

5 

4  045085 

2  938925 

i  4  019130  2  974000 

5 

I  C 

4  854102 

3  526710 

;  4  822956 3  568800 

'  6 

I  7 

5  7G3119 

I   114495 

I  5  62G782'4  163600 

/ 

;    8 

G  472136 

4  7022hO 

;  6  430608  4  758400 

8 

^  9 

7  28115315  290065 

i  7  234434  5  353200 

9 

Ji  TRArLIlJ^L  1ABLL. 


] 

Latitude. 

Departure.  | 

Latitude.  1  Departure. 

Di5-t. 

1  1 

63o 

37*"^    ! 

520  30'   370  30/ 

Dist. 

0.798636 

'J.601815   I 

0.793323 

0. 608738 

1 

2 

1  597272 

1  203630  i 

1  586646 

1  217476 

0 

3 

2  395908 

1  805445 

2  379969 

1  826214 

3 

4 

3  194344 

2  4072G0  1 

3  173292 

2  434952 

4 

5 

3  993180 

3  009075   ! 

3  966615 

3  043690 

5" 

6 

4  7918161 

3  610890  1 

4  759938 

3  652428 

6 

7 

5  5902521 

4  212705   i 

5  5  53261 

4  261166 

7 

8 

6  38SGSS 

4  814580  ; 

6  346584 

4  869904 

8 

9 

7  187524 

5  41G335  ! 
38o    \ 

'  7  139907 

'5  478642 

9 

52^ 

'   51o  30' 

1  0.782578 

38°  30' 

1 

0.78801110.616661   i 

0.622490 

1 

o 

1  576022,1  231322  { 

1  565156 

I  214980 

2 

3  i 

2  364033 

1  846983  i 

'  2  347734 

1  867470 

3 

4 

3  152044 

2  462644  1 

:  3  130312 

2  489960 

4 

6 

3  940055 

3  078305"  ' 

;  3  93  2890 

3  112450 

5 

G 

4  728066 

3  693965  • 

4  695468 

3  734940 

6 

I  7 

5  516077 

4  309C27 

j  5  478046 

4  357430 

7 

■  8 

6  304038 

4  9252S8  1 

j  6  260624 

4  979920 

8 

9 

7  092099 
51o 

5  540349  1 

!  7  043202 

5  C02410 

9 

^  3St* 

1 

1   500  30' 

39-  30' 

1 

0.777 146!0. 629320  | 

1  0.7  71595 

0.636054 

1 

2 

1  5542021 1  25SG40  i 

!  1  543190 

1  272108 

0 

3 

2  331438jl  887960 

1  2  314785 

1  908162 

3 

4 

3  108544  2  517280 

1  3  086380 

2  544216 

4 

5 

3  8  85730;3  146600 

1  3  857975 

3  180270 

5 

6 

4  062876:3  775920 

1  4  629570 

3  816324 

6 

7 

5  440022J4  205240  j 

5  401165 

4  452378 

7 

8 

0  21 71GSJ5  034560  1 

6  172760 

5  088432 

8 

9 

6  994314j5  663880  < 

6  944S55 

5  72448  6 

9 

50o. 

40o 

1   490  30' 

1 

40-'  30' 

1 

0.766044 

0.642788 

1  0.760377 

0.649423 

1 

2 

1  532088 

,1  285576 

1  520754 

1  298846 

2 

3 

2  298132 

il  928364 

2  281131 

I  948269 

3 

3 

3  064176 

2  571152 

3  041508 

2  597692 

4 

3 

3  8.S0220 

3  213940 

3  801885 

3  247115 

5 

G 

4  596264 

3  8  5  6728 

4  562262 

3  896538 

6 

7 

5  3o2308 

4  499516  { 

5  322639 

i   545961 

7 

8 

6  1282.52 

5  142304 

6  083016 

5  195384 

8 

9 

6  894396 

5  785092 

6  843393 

5  844807 

9 

113 


A  TRAl 


>i.   TABLE. 


— ;^;- 

i.rt             De,. 

L.-..         \)vv.        1 

Lu*., 

C 

F 

,190             ^^Q. 

■;       .^  .','  ;  41GJG' 

4n<^ 

1 

'                           1 
U.7547IUO.60GO59     i 

0.748927 10.66  2595 

0.707107 

1 

o 

I  50i<420 

■1  312113 

-  1497  354 11325190 

1  414214 

0 

i2o4130 

1  968177 

%  241)78111  987785 

2 121321 

3 

4 

3  01G840 

2  624236 

'     $995708  2  650380 

2  828428 

4 

5 

3  773550  3  'iyJil'o 

\  .  3  7446-3513  3121^75 

3  535535 

5 

.0- 

4  52^:^60  3  P36.3o4 

4  49353213  975570 

4  242642 

6 

7 

5  CSL>^-70  4  53W413 

5  242489  4  638165 

4  949749 

8  . 

ti  037Ct(«  5  2J8472 

5  991816  5  300760     ii5  6.368.56 

8 

0    ' 

ti  7G:;:o90 

5  904531 

6  740343  5  'J'a-.iobb     i 

6  363963 

9 

4^^ 

.^00 

i      47^^30'    42«^'30'       \ 

'                                          1 

* 

1 

0.7431-^5  0.669131 

0.7.37249lo.675564     | 

1 

2 

1  486-290  1  338-^62 

,    -1  47449:;;!. 351128     ! 

2 

2  239435  2  007393 

:     2  21 1747 '-2  026692     ' 

3 

4 

2  97258U  2  676324 

.     2  948996  0  702256 

.     4 

5 

3  715725  3  346655 

:     3  686245J3  379920 

!     5 

t> 

4  458370  4  014786 

4  4234-94;  4  053384 

!    6 

1 

5  202015  4  6S3S17 

5  16074.314^18948 

j  ' 

O 

5  945160  i  o53i)48 

5  897992ir,  404512 

0 

0 

0 

6  688205  6  023179 

1      6  634241 -6  080076 

1 

9 

1 

t 

i     1 

470          43^ 

1       4 GO  39'    430  30' 

0.731351 

10.681998 

:     0.725347,0.688328 

v> 

1  4G2708 

|1  363996 

'      1  4.30794i  i  SiQQB^ 

i 

2 

3 

2  KM062 

2  045094 

\   2  i76o-n:2  06^ir.84 

i 

L> 

4 

■2  925416 

2  727992 

1      2  8013^8  2  75 JS 12 

i 

■     4 

5 

3  656770 

3  409990 

!      3  626735  3  441640 

i     5 

G 

4  38S124;  1091988 

j;     4  352082|4  129968 

1    c 

i 

5  119478  4  773986 

!;     5  077429;4  81S29G 

•     7 

8 

.5  8508.32.5  4559>i4 

5  802776  5  .5vW624 

8 

9 

•r5:^218o;6  137932 

'     6  528 12J 6  194952 

Lat. 
88^ 

io.999391 

'' 

46^     i     4.1'"> 

1 

450  30'     44036' 

! 

0.7;  3223  !o,700882 

i 

1 

.     1 

1 
0.719.i-?i)i0.694658 

1 

-> 

I  4JJ680 

1  389316 

i     1  4  26446  1  401764 

1.998782 
2  998173 

2 

o 

2  15'Ji>20 

2  08.3974 

j     2  139669,-2  102646 

0 
.> 

4 

2  877360 

2  7786.52 

;     2  5L52<92;2  803528 

,3  997564 

4 

5 

3  596700  3  47.3230 

.     3  566125:3  504410 

!4  ^daros 

5 

6 

4  316040  4  167948 

1     4  27933Ki4  2a32<:»2 

'5  9i>(j:i'\C 

i     6 

< 

.3  035380!4  862606 

!     4  992561 14  906174 

6  9957. '57 

1 

8 

5  7.S4720  5  557264 

'     5  70578415  G07056 

7  99512k 

8 

0 

6 474060  G 251922 

,     6  419007  6  307938 

8  994519 

» 

119 


CONTENTS. 


Page 

Construction  of  iho  Plain  Scale,  -         -         -  10 

Ho;v  to  prove  the  Sliding  Rule,  -         -         —  12 

Gunter's  Scale,  -  _         _         _         _  J3 

Dejicription  anil  Use  of  the  Sector,  —         —  17 

Use  of  the  Lines  of  Sine*,  Tangents,  and  Secants,  20 

IjP  of  the  Line  of  Polys^ons,  -         -         —         21 

Ll^e  of  the  Sector  in  Trigonometry,  -         —  22 

*'~"  .^Of  the  Sliding  Rule,  -     "   .    -  ->  -  '?2 

^.lT!%nsa  ration,  -  -  -  —  —  32 

.*       Trailing  of  Casks,  —  -  -  -  38 

*,^_  Giiaging  Casks  by  the  Sliding  Rule,  -  —  45 

''-w^  ^^'P^ihle  for  the  use  of  Coopers,  in  calculating  Cisterns,  49 

A  Log  Table,  showing  the   number  of  feet  of  boards, 

any  log  will  make,  —  —  _  50 

A  Table  of  Specific  Gravities  of  Bodies,  —  51 

Of  a  Table  of  Solid  Measure  of  Square  Timber,  52 

A  Table  of  Square  Timber,  —  _         54 

Of  the  Weight  and  Dimensions  of  Ralls,  -         61 

Of  a  Table  of  Solid  measure,  of  Round  Timber,  62 

A  Table  of  Round  Timber,  -  -         -         68 

A  Table  giving  the  Side  of  a  Square,  equal  to  a  Square, 

in'=cribed  in  a  given  Circle,  -  —         85 

Of  S'lrveying,  -  -  -  _         gg 

Of  Logarithms,  —  -  —  _  94 

A  Table  of  Logarithms,  -  -  _        100 

Of  a  Traverse  Table   or  Ditference  of  Latitude  and 

Dpparture,  -  -  _  _       ]05 

A  Traverse  Table,         -  -  -  -       107 


ERRATA.  The  61  and  62  pages,  shotild  have  been  in  the  place  of 
the  66  and  67  pairet,  or  between  the  tables  of  square  timber  and 
rouuil  timber. — The  line  at  the  bottom  of  the  87  pa^e  should  be  at 
the  top.  —In  the  Traverse  table,  pa^e  108,  under  8S  de,^rees  Lati- 
tude, i?  wron-r,  and  it  will  be  found  corrected,  under  Latitude  45  de- 
gree?, page  118. 


/ 

h 


M^^ 


■.^ 


